H C VERMA Solutions for Class 12-science Physics Chapter 10 - Electric Current in Conductors

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Chapter 10 - Electric Current in Conductors Exercise 198

Question 1

The amount of charge passed in time t through a cross-section of a wire is

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

(a) Write the dimensional formulae for A, B and C.

(b) If the numerical value of A, B and C are 5, 3 and 1 respectively in SI units, find the value of current at H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Solution 1

(a) [Q]=[A][T]2=[B][T]=[C]

[I][T]=[A][T]2=[B][T]=[C]

[A]=[IT-1]

[B]=[I]

[C]=[IT]

(b) H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

I=2At+B

I=2(5)(5)+3

I=53A

Question 2

An electron gun emits H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductorselectrons per second. What electric current does this correspond to?

Solution 2

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 3

The electric current existing in a discharge tube is 2.0 μA. How much charge is transferred across a cross-section of the tube in 5 minutes?

Solution 3

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 4

The current through a wire depends on time as

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Where H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors andH-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors. Find the charge crossed through the section of the wire in 10 seconds.

Solution 4

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 5

A current of 1.0 A exists in a copper wire of cross-section 1.0mm2. Assuming one free electron per atom calculate the drift speed of the free electrons in the wire. The density of copper is 9000kg/m3.

Solution 5

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

Now,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 6

A wire of length 1m and radius 0.1mm has a resistance of 100Ω. Find the resistivity of the material. 

Solution 6

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In ConductorsΩ.m 

Question 7

A uniform wire of resistance 100Ω is melted and recast in a wire of length double that of the original. What would be the resistance of the wire? 

Solution 7

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In ConductorsΩ 

Question 8

Consider a wire of length 4m and cross-sectional area 1mm2 carrying a current of 2A. If each cubic meter of the material contains H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors free electrons, find the average time taken by an electron to cross the length of the wire.

Solution 8

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors m/s

Now,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

Question 9

What length of a copper wire of cross-sectional area 0.01mm2 will be needed to prepare a resistance of 1 kΩ?H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors Ω-m.

Solution 9

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 10

Figure (32-E1) shows a conductor of length l having a circular cross-section. The radius of cross-section varies linearly from a to b. the resistivity of the material is ρ. Assuming that b-a<<l, find the resistance of the conductor.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 10

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Resistance of the small strip

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors -(i)

Now,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Differentiate with respect to x

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Now,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 11

A copper wire of radius 0.1mm and resistance 1kΩ is connected across a power supply of 20 V. (a) How many electrons are transferred per second between the supply and the wire at one end? (b) Write down the current density in the wire.

Solution 11

(a) H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

(b) H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 12

Calculate the electric field in a copper wire of cross-sectional area 2.0mm2 carrying a current of 1A. The resistivity of copper=1.7×10-8Ω-m.

Solution 12

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 13

A wire has a length of 2.0m and a resistance of 5.0Ω. Find the electric field existing inside the wire if it carries a current of 10A. 

Solution 13

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 14

The resistances of an iron wire and a copper wire at 20°C are 3.9Ω and 4.1 Ω respectively. At what temperature will the resistances be equal? Temperature coefficient of resistivity for iron is 5.0×10-3 K-1 and for copper it is 4.0×10-3 K-1. Neglect any thermal expansion.

Solution 14

Resistance at temperature T is given by H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Let, at temperature T

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 15

The current in a conductor and the potential difference across its ends are measured by an ammeter and a voltmeter. The meters draw negligible currents. The ammeter is accurate but the voltmeter has a zero error (that is, it doesn't read zero when no potential difference is applied). Calculate the zero error if the readings for two different conditions are 1.75 A, 14.4 V and 2.75 A, 22.4 V

Solution 15

Voltmeter reading=zero error + potential due to current

14.4=V+(1.75)R (i)

22.4=V+(2.75)R (ii)

Subtract (ii) from (i)

8=R

Put value in (i)

14.4=V+(1.75)8

V=0.4 volt

Question 16

Figure (32-E2) shows an arrangement to measure the emf ε and internal resistance r of battery. The voltmeter has a very high resistance and ammeter also has some resistance. The voltmeter reads 1.52 V when the switch S is open. When the switch is closed the voltmeter reading drops to 1.45 V and ammeter reads 1.0 A. find the emf and internal resistance of the battery.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 16

Initially, no current flows in circuit when switch is open.

So, emf of cell=voltmeter reading

ε=1.52V

Now, when switch is closed, cell is discharging

So, TPD=ε-ir

1.45=1.52-(1)(r)

r=0.07Ω 

Question 17

The potential difference between the terminals of a battery of emf 6.0 V and internal resistance 1 Ω drops to 5.8 V when connected across an external resistor. Find the resistance of an external resistor. 

Solution 17

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

For battery

TPD=ε-ir

5.8=6-i(1)

i=0.2A

for external resistor

V=IR

5.8=(0.2)(R)

R=29Ω 

Chapter 10 - Electric Current in Conductors Exercise 199

Question 18

The potential difference between the terminals of a 6.0 V battery is 7.2 V when it is being charged by a current of 2.0 A. What is the internal resistance of the battery?

Solution 18

TPD=ε+ir

7.2=6+(2)(r)

r=0.6Ω 

Question 19

The internal resistance of an accumulator battery of emf 6V is 10Ω when it is fully discharged. As the battery gets charged up, its internal resistance decreases to 1Ω. The battery in its completely discharged state is connected to a charger which maintains a constant potential difference of 9V. find the current through the battery. (a)Just after the connections are made and (b) After a long time when it is completely charged.

Solution 19

(a) Net emf across battery=9-6=3V,

Req=10Ω

current=3/10=0.3A

(b) Net emf across battery =9-6=3V

Resistance = 1Ω 

Current=3/1=3A

Question 20

Find the value of i1/i2 in figure (32-E3) if (a) R=0.1Ω (b)R=1Ω (c) R=10Ω.Note from your answers that in order to get more current from a combination of two batteries they should be joined in parallel if the external resistance is small and in series if the external resistance is large as compared to the internal resistances.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 20

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Cells are in series combination

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

So, H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

cells are in parallel combination

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Divide (i) and (ii)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

(a) H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

(b) H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

(c) H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 21

Consider H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors identical cells, each of emf ε and internal resistance r. Suppose n1 cells are joined in series to form a line and n2 such lines are connected in parallel. The combination drives a current in an external resistance R. (a) Find the current in external resistance. (b) Assuming that n1 and n2 can be continuously varied, find the relation between n1, n2, R and r for which the current in R is maximum.

Solution 21

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

For I to be maximum,H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors will be minimum

To minimize,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

Differentiate wrtH-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 22

The battery of emf 100 V and a resistor of resistances 10kΩ are joined in series. This system is used as a source to supply current to an external resistance R. If R is not greater than 100Ω, the current through it is constant up to two significant digits. Find its value. This is the basic principle of a constant-current source 

Solution 22

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Emf=100V

Req= 10000+R

Current H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

For R=1Ω 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

For R=100Ω 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

So up to R=100Ω the current does not change up to 2 significant figures. 

Question 23

If the reading of ammeter A1 in figure (32-E4) is 2.4 A, what will the ammeters A2 and A3 read? Neglect the resistances of the ammeter.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 23

Voltage drop access A1=voltage drop access A2

I1R1=I2R2

(2.4)(20)=I2(30)

I2=1.6A

Reading in A3=reading in A1+reading in A2

=(2.4)+(1.6)

=4A

Question 24

The resistance of the rheostat shown in figure (32-E5) is 30 Ω. Neglecting the meter resistance; find the minimum and maximum currents through the ammeter as the rheostat is varied.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 24

Emf=5.5V

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

for minimum currentH-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Now, for maximum current H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 25

Three bulbs, each having a resistance of 180Ω,are connected in parallel to an ideal battery of emf 60 V. find the current delivered by the battery when (a) all the bulbs are switched on, (b) two of the bulbs are switched on and (c) Only one bulb is switched on.

Solution 25

For each bulb

Voltage applied=60V

Resistance=180Ω 

Current I=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

(a) All bulbs switched on

IN=I1+I2+I3

IN=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

(b) Two bulbs switched on

IN=I1+I2

=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

=0.67A

(c) Only one bulb switched on

IN=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors=0.33A

Question 26

Suppose you have three resistors of 20Ω, 50Ω and 100Ω. What minimum and maximum resistances can you obtain from these resistors? 

Solution 26

For maximum resistance all will be in series combination

Req=20+50+100=170Ω 

For minimum resistance all will be in parallel combination

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 27

A bulb is made using two filaments. A switch selects whether the filaments are used individually or in parallel. When used with a 15 V battery, the bulb can be operated at 5 W, 10 W or 15 W. What should be the resistances of the filaments?

Solution 27

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

When bulbs are used in parallel, the equivalent resistance will be less than their individual resistance

two resistances are 45Ω and 22.5Ω 

Question 28

Figure (32-E6) shows a part of a circuit. If a current of 12 mA exists in the 5kΩ resistor, find the currents in the other three resistors. What is the potential difference between the points A and B?

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 28

Let I be the current in 20kΩ 

So(12-I) will be current in 10kΩ 

Now, V20kΩ=V10kΩ(parallel combination)

I(20)=(12-I)(10)

I=4mA

So,

I20kΩ=4mA

I10kΩ=8mA

I100kΩ=12mA

Equivalent resistance between AB

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

VAB=IH-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

=(12×10-3)(111.67×103)

VAB=1340V

Question 29

An ideal battery sends a current of 5A in a resistor. When another resistor of value 10Ω is connected in parallel, the current through the battery is increased to 6A. Find the resistance of the first resistor. 

Solution 29

Initially,

V=IR

V=5R -(i)

Now, when 10Ω is connected in parallel to R 

V=IReq

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

From (i) and (ii)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

R=2Ω 

Question 30

Find the equivalent resistance of the network shown in figure (32-E7) between the points a and b.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 30

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 31

A wire of resistance 15.0Ω is bent to form a regular hexagon ABCDEFA. Find the equivalent resistance of the loop between the points (a) A and B, (b) A and C and (c) A and D.

Solution 31

Resistance of each side of hexagon=15/6=2.5Ω

(a)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

RAB=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

(b)

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

RAC=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

 

(c)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

RAD=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

Question 32

Consider the circuit shown in the figure (32-E8). Find the current through the 10Ω resistor when the switch S is (a) Open and (b) Closed.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 32

(a) Req=10+20=30Ω 

V=3 volt

V=IR

3=I(30)

I=0.1A

(b) Req=10Ω

V=IR

3=I(10)

I=0.3A

Chapter 10 - Electric Current in Conductors Exercise 200

Question 33

Find the currents through the three resistors shown in figure (32-E9).

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 33

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Emfeq=4-2=2V

Req=4+6=10Ω 

CurrentH-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 34

Figure (32-E10) shows a part of an electric circuit. The potentials at the points a, b and c are 30V, 12V and 2V respectively. Find the currents through the three resistors.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 34

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Potential at X

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 35

Each of the resistors shown in figure (32-E11) has a resistance of 10Ω and each of the batteries has an emf of 10V. Find the currents through the resistors a and b in the two circuits.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

 

Solution 35

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

(a) For resistor a,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

For resistor b,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

(b)

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

For resistor a,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

For resistor b,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 36

Find the potential difference (Va-Vb) in the circuits shown in figure (32-E12).

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 36

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

(a) Both cells are in parallel combination

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Internal resistance of cell will be

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Equivalent Resistance of circuit

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

So, current

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Voltage difference across ab

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

(b) The circuit can be redrawn as shown in figure

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

It is similar to above circuit in (a).

Hence same answer.

Question 37

In the circuit shown in figure (32-E13), ε1 = 3V, ε2 = 2V, ε3 = 1V and r1=r2=r3=1Ω. Find the potential difference between the points A and B and the current through each branch.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 37

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

KVL for loop 1

3-I1(1)+I2(1)-2=0

I1-I2=1 -(i)

KVL for loop 2

2-I2(1)-( I1+I2)(1)-1=0

I1-2I2=1 -(ii)

Solving (i) and (ii)

I1=1A and I2=0A

Now,

VAB=TPD for cell of 2V

= ε-ir

= 2-(0)(1)

VAB = 2V

Question 38

Find the current through the 10Ω resistor shown in figure (32-E14)

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 38

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

 

Potential at point of X volt

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Solving, X=3V

Current in 10Ω resistance=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 39

Find the current in the three resistors shown in figure (32-E15).

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 39

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Potential difference across each resistance is 0

So, current =0

Question 40

What should be the value of R in figure (32-E16) for which the current in it is zero?

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 40

The circuit is in wheat stone symmetry

So, for all values of R, current=0.

Question 41

Find the equivalent resistance of the circuits shown in figure (32-E17) between the points a and b. Each resistor has a resistance r.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

 

Solution 41

(a)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

(b)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 42

Find the current measured by the ammeter in the circuit shown in the figure (32-E18).

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

 

Solution 42

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

The 50R resistors are in wheat stone symmetry, so no current flows in them

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Chapter 10 - Electric Current in Conductors Exercise 201

Question 43

Consider the circuits shown in (32-E19a). Find

(a) The current in the circuit,

(b) The potential drop across the 5Ω resistor, 

(c) The potential drop across the 10Ω resistor. 

(d) Answer the parts (a), (b) and (c) with reference to figure (32-E19b).

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 43

(a) (Emf)eq = 12+6 = 18V

Req = 10+5 = 15Ω 

Current I = H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

(b) Now,H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

(c) H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

(d) Circuit in figure (b) is same as in figure (a)

Question 44

Twelve wires, each having equal resistance r, are joined to form a cube as shown in figure (32-E20). Find the equivalent resistance between the diagonally opposite points a and f.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 44

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Apply KVL for abcfa

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 45

Find the equivalent resistances of the networks shown in figure (32-E21) between the points a and b.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 45

(a)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

 

(b)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

 

(c)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

 

(d)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

 

(e)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 46

An infinite ladder is constructed with 1Ω and 2Ω resistors as shown in figure (32-E22). 

(a) Find the effective resistance between the points A and B.

(b) Find the current that passes through the 2Ω resistor nearest to the battery.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

 

Solution 46

(a)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Let equivalent resistance between AB be x

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

(b)

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

I=V/R=6/2=3A

Current in 2Ω 

I2Ω=3/2=1.5A

Question 47

The emf ε and the internal resistance r of the battery shown in figure (32-E23) are 4.3V and 1.0Ω respectively. The external resistance R is 50Ω. The resistances of the ammeter and voltmeter are 2.0Ω and 200Ω respectively. 

(a) Find the readings of the two meters.

(b) The switch is thrown to the other side. What will be the readings of the two meters now?

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 47

(a)

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Current, H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors(Ammeter reading)

Now,50Ω and 200Ω are in parallel combination 

So, current is divided in inverse Ratio

current in voltmeter=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

= H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors=0.02A

Voltmeter reading =(0.02)(200)=4V

(b)

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Current, H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors(Ammeter reading)

TPD across cell=voltmeter reading

Voltmeter reading= ε-Ir=4.3-0.08(1)=4.2V

Question 48

A voltmeter of resistance 400Ω is used to measure the potential difference across the 100Ω resistor in the circuit shown in figure (32-E24). 

(a) What will be the reading of voltmeter?

(b) What was the potential difference across 100Ω before the voltmeter was connected?

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 48

(a) H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Since, 100Ω and 400Ω are in parallel combinationso, current is divided in inverse Ratio of resistances.

current in voltmeter Iv=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Voltmeter reading H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors=24V

(b)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

So,

V100Ω=IR=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

Question 49

The voltmeter shown in figure (32-E25) reads 18V across the 50Ω resistor. Find the resistance of the voltmeter.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 49

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

I24Ω=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

I50Ω=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

I24Ω= I50Ω+Iv [by KCL]

0.5=0.36+Iv

Iv=0.14A

For voltmeter,

Vv=IvRv

18=0.14R

Rv130Ω 

Question 50

A voltmeter consists of a 25Ω coil connected in series with a 575Ω resistor. The coil takes 10 mA for full scale deflection. What maximum potential difference can be measured on this voltmeter? 

Solution 50

Req=25+575=600Ω;I=10mA 

V=IR

V=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

V=6 volt

Question 51

An ammeter is to be constructed which can read currents up to 2.0A. If the coil has a resistance of 25Ω and takes 1mA for full-scale deflection, what should be the resistance of the shunt used? 

Solution 51

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

IgRg=(I-Ig)Rs

(10-3)(25)=(2-10-3)Rs

Rs=1.25×10-2R

Question 52

A voltmeter coil has resistance 50.0Ω and resistor of 1.15kΩ is connected in series. It can read potential differences up to 12 volts. If this same coil is used to construct an ammeter which can measure currents up to 2.0A, what should be the resistance of the shunt used? 

Solution 52

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

V=Ig(Rg+R)

12=Ig(50+1150)

Ig=0.01A

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Now, IgRg=(I-Ig)Rs

(0.01)(50)=(2-0.01)Rs

Rs=0.25R

Question 53

The potentiometer wire AB shown in figure (32-E26) is 40cm long. Where the free end of the galvanometer should be connected on AB so that the galvanometer may show zero deflection?

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 53

At null deflection, it will be in wheat-stone symmetry.

Let l be the balancing length from end A

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Chapter 10 - Electric Current in Conductors Exercise 202

Question 54

The potentiometer wire AB shown in figure (32-E27) is 50cm long. When AD = 30cm, no deflection occurs in the galvanometer. Find R.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 54

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 55

A 6 volt battery of negligible internal resistance is connected across a uniform wire AB of length 100cm. The positive terminal of another battery of emf 4V and internal resistance 1Ω is joined to the point A as shown in the figure (32-E28). Take the potential at B to be zero. 

(a) What are the potentials at the points A and C?

(b) At which point D of the wire AB, the potential is equal to the potential at C?

(c) If the points C and D are connected by a wire, what will be the current through it?

(d) If the 4V battery is replaced by 7.5V battery, what would be the answers of parts (a) and (b)?

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 55

(a)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

VA=6V

VC=2V

 

(b) Potential across AD=Potential across AC=4V

Potential across DB=2V

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

(c) No current will flow as VC=VD

 

(d) Potential difference across AC=potential at A-potential at C

7.5=6-Vc

VC=-1.5V

No points exist on wire AB as potential difference. Wire isalways greater than or equal to zero.

Question 56

Consider the potentiometer circuit arranged as in figure (32-E29). The potentiometer wire is 600cm long.

(a) At what distance from the point A should the jockey touch the wire to get zero deflection in the galvanometer?

(b) If the jockey touches the wire at a distance of 560cm from A, what will be the current in the galvanometer?

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 56

(a) Reqfor primary circuit=r+15r=16r

Current=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

VAB=IR

VAB=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Potential gradient H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Let balancing length be l from end A.

Emf=xl

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

(b)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Resistance of 560cm wire = H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Resistance of 40cm wire=15r-14r=r

Nodal analysis at X

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Potential difference across resistance r

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 57

Find the charge on the capacitor shown in figure (32-E30).

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 57

In steady state, no current flows through capacitor

Req=10+20=30Ω 

V=IR

2=I(30)

I=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

Voltage across capacitor=voltage across 10Ω 

=IR

=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

Q=CV

Q=6H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

Question 58

Find the current in the 20Ω resistor shown in figure (32-E31).If a capacitor of capacitance 4 μF is joined between the points A and B, what would be the electrostatic energy stored in it in steady state.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 58

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Nodal analysis at X

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

For 20Ω resistor  

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 59

Find the chargers on the four capacitors of capacitances 1 μF, 2 μF, 3 μF and 4 μF shown in figure (32-E32).

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 59

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

1Ω and 2Ω resistors are in series combination 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

So, potential across 1H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors=potential for 1Ω

=1×2=2volt

So, charge=CV=(1)(2)=2μC

Potential across 2μF=potential diff for 2Ω 

=2×2=4V

So, charge=CV=(2)(4)=8μC

Now, for 3Ω-3Ω resistors, 

Potential drop across each resistance is 3V

Charge on 3μF capacitor=CV

=(3μF)(3)=9μC

Charge on 4μF capacitor=CV

=(4μF)(3)=12μC

Question 60

Find the potential difference between the points A and B and between the points B and C of figure (32-E33) in steady state.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 60

No current flows in steady state

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Nodal analysis at X

(X-100)3+(X-100)3+(X-0)1+(X-0)1=0

8X=600

X=75

VA-VB=100-75

=25V

VB-VC=75-0

=75V

Question 61

A capacitance C, a resistance R and an emf ε are connected in series at t=0. What is the maximum value of,

(a) The potential difference across the resistor,

(b) The current in the circuit,

(c) The potential difference across the capacitor,

(d) The energy stored in the capacitor,

(e) The power delivered by the battery and

(f) The power converted into heat.

Solution 61

(a) Maximum potential difference across resistor=ε

When charge on capacitor is 0

(b) At t=0, capacitor acts as short circuit

VR=ε=IR

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

(c) At t=, capacitor acts as open circuit 

Vmax-cap.=ε

(d) H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors (at t=,Vcap=ε)

(e) Power=εI

Pmax=εImax

Pmax=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

(f) Power dissipated=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 62

A parallel-plate capacitor with plate area 20cm2 and plate separation 12.0mm is connected to a battery. The resistance of the circuit is 10 kΩ. Find the time constant of the circuit. 

Solution 62

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 63

A capacitor of capacitance 10 μF is connected to a battery of emf 2V. It is found that it takes 50ms for the charge on the capacitor to become 12.6 μC. Find the resistance of the circuit.

Solution 63

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 64

At 20 μF capacitor is joined to a battery of emf 6.0V through a resistance of 100Ω. Find the charge on the capacitor 2.0 ms after the connections are made. 

Solution 64

Q = Q0(1-H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors)

= (20H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

= 12H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

= 76μC

Question 65

The plates of a capacitor of capacitance 10μF, charged to 60μC, are joined together by a wire of resistance 10Ω at t=0. Find the charge on the capacitor in the circuit at  

(a) t = 0,

(b) t = 30 μs,

(c) t = 120 μs and

(d) t = 1.0 ms

Solution 65

Q = Q0H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

Q = 60 H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

Q = 6H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

(a) t = 0

Q = 6H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

(b) t = 30μs

Q = 6 H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

Q = 44μC

(c) t = 120μs

Q = (6 H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

= 18μC

(d) t = 1ms

Q = (6 H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

= 0.003μC

Question 66

A capacitor of capacitance 8.0 μF is connected to a battery of emf 6.0V through a resistance of 24Ω. Find the current in the circuit 

(a) Just after the connections are made and

(b) One time constant after the connections are made

Solution 66

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

(a) H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

(b) H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Chapter 10 - Electric Current in Conductors Exercise 203

Question 67

A parallel-plate capacitor has plate area 40cm2 and separation between the plates 0.10mm is connected to a battery of emf 2.0V through a 16Ω resistor. Find the electric field in the capacitor 10ns after the connections are made. 

Solution 67

Capacitance

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Time constant

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Electric field in capacitor =H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

Question 68

A parallel-plate capacitor has plate area 20cm2, plate separation 1.0mm and a dielectric slab of dielectric constant 5.0 filling up the space between the plates. This capacitor is joined to a battery of emf 6.0v through a 100kΩ resistor. Find the energy of the capacitor 8.9μs after the connections are made. 

Solution 68

Capacitance

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

charge

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

time constant =RCH-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Energy stored=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 69

A 100μF capacitor is joined to a 24V battery through a 1.0MΩ resistor. Plot qualitative graphs 

(a) Between current and time for the first 10 minutes and

(b) Between charge and time for the same period

Solution 69

(a)

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

at t=0,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

At t=10×60=600sec.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

(b)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

at H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

at H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 70

How many times constants will elapse before the current in a charging RC circuit drops to half of its initial value? Answer the same question for a discharging RC circuit.

Solution 70

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

For discharging, H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductorsso, answer will be same.

Question 71

How many times constants will elapse before the charge on a capacitor falls to 0.1% of its maximum value in a discharging RC circuit?

Solution 71

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 72

How many times constants will elapse before the energy stored in the capacitor reaches half of its equilibrium value in a charging RC circuit?

Solution 72

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 73

How many time constants will elapse before the power delivered by the battery drops to half of its maximum value in an RC circuit?

Solution 73

Power=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

VI=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

I=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

Question 74

A capacitor of capacitance C is connected to a battery of emf ε at t=0 through a resistance R. Find the maximum rate at which energy is stored in the capacitor. When the rate doeshave this maximum value?

Solution 74

Energy stored,H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Rate of energy stored=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

For maximum rate of energy stored

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Put in (i)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 75

A capacitor of capacitance 12.0μF is connected to a battery of emf 6.00V and internal resistance1.00Ω through resistance less leads. 12.0μs after the connections are made, what will be  

(a) The current in the circuit,

(b) The power delivered by the battery,

(c) The power dissipated in heat and

(d) The rate at which the energy stored in the capacitor is increasing.

Solution 75

(a) H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

(b) P=VI

=(6)(2.21)

P=13.25W

(c) Power dissipated=I2R

=(2.21)2(1)

=4.87W

(d) Energy stored H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 76

A capacitance C charged to a potential difference V is discharged by connecting its plates through a resistance R. Find the heat dissipated in one time constant after the connections are made. Do this by calculating H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors and also by finding the decrease in the energy stored in capacitor.

Solution 76

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

Heat dissipated H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

By energy method:-

Heat dissipated= energy stored at t=0-energy stored at time t

=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 77

By evaluating H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors, show that when a capacitor is charged by connecting it to a battery through a resistor, the energy dissipated as heat equals the energy stored in the capacitor.

Solution 77

Current in circuit at time t,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Heat dissipated

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 78

A parallel-plate capacitor is filled with a dielectric material having resistivity ρ and dielectric constant K. The capacitor is charged and disconnected from the charging source. The capacitor is slowly discharged through the dielectric. Show that the time constant of the discharge is independent of all geometric parameters like the plate area or separation between the plates. Find this time constant.

Solution 78

Capacitance

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

resistance of dielectric material,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

time constant

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

It is independent of geometric parameters

Question 79

Find the charge on each of the capacitors 0.20 ms after the switch S is closed in figure (32-E34).

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

 

Solution 79

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

So, charge on each capacitor=18.4/2=9.2μC

Question 80

The Switch S shown in figure (32-E35) is kept closed for a long time and is then opened atH-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors. Find the current in the middle 10Ω resistor at H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 80

Initially, the capacitor was charged completely

Potential across capacitor=Potential across 10Ω  

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

chargeH-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Now, capacitor is discharged

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 81

A capacitor of capacitance 100μF is connected across a battery of emf 6.0 V through a resistance of 20kΩ for 4.0s. The battery is then replaced by a thick wire. What will be the charge on the capacitor 4.0s after the battery is disconnected?  

Solution 81

During charging, charge developed in 4sec

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Now discharging

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 82

Consider the situation shown in figure (32-E36). The switch is closed at H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors when the capacitors are uncharged. Find the charge on the capacitor C1 as a function of time t.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Solution 82

Equivalent capacitance

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 83

A capacitor of capacitance C is given a charge Q. AtH-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors, it is connected to an uncharged capacitor of equal capacitance through a resistance R. Find the charge on second capacitor as a function of time.

Solution 83

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

 

Let charge on capacitor B at time t be q

Applying KVL,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors

Question 84

A capacitor of capacitance C is given a charge Q. AtH-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors, it is connected to an ideal battery of emf ε through a resistance R. Find the charge on capacitor at time t.

Solution 84

Initial charge given to the capacitor=Q

When the capacitor is connected by a battery, it will charge through the battery. The initial charge will also delay.

Growth of charge by battery

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

Delay of charge through capacitor

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors 

Net charge on capacitor at time H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current In Conductors