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Class 10 LAKHMIR SINGH AND MANJIT KAUR Solutions Physics Chapter 1 - Electricity

Electricity Exercise 5

Solution 1

Volt

Solution 2

(b) a volt is a joule per coulomb.

Solution 3

(a) p.d. stands for potential difference.
(b) Voltmeter is used to measure p.d.

Solution 4

Electric potential at a point is 1 volt means 1 joule of work is done in moving 1 unit positive charge from infinity to that point.

Solution 5

Potential difference = 1 V

Charge moved = 1C

 

Work done = Potential difference x Charge moved

                = 1 x 1 = 1 J

Solution 6

Volt

Solution 7

Given,

Potential difference = 12 V,  Charge moved = 2 C

We know that, 

Work done= p.d. x charge moved

                = 12 x 2

                = 24 joules

Solution 8

Coulomb

Solution 9

One coulomb of charge is that quantity of charge which exerts a force of 9 x 109 Newton on an equal charge is placed at a distance of 1 m from it.

Solution 10

(a) volts; voltmeter; parallel

(b) conductor; insulator

Solution 11

Conductors:- Those substances through which electricity can flow are known as conductors. E.g., Copper, silver etc.

Insulators:- Those substances through which electricity cannot flow are known as insulators. E.g., Plastic, cotton etc.

Solution 12

Conductor:- Silver, Copper, Aluminum, Nichrome, Graphite, Mercury, Manganin

Insulators:- Sulphur, Cotton, Air, Paper, Porcelain, Mica, Bakelite, Polythene

Solution 13

The electric potential (or potential) at a point in an electric field is defined as the work done in moving a unit positive charge from infinity to that point.

Unit of electric potential is volt.

Solution 14

(a)

      (b) V1=220 V, V2=230V, Charge moved=4C

           Thus, the potential difference= V2- V1

                                        =230-220

                                        =10V

           We know that,  

           Work done = Potential difference x Charge moved

                            = 10 x 4

           Work done = 40 joules

Solution 15

(a) Voltmeter

(b) Given :  Potential difference=12V, Charge moved=1C

We know that,   

Work done = Potential difference x charge moved

                 = 12 x 1 = 12 joules

Since work done on each coulomb of charge is 12 joules, the energy given to each coulomb of charge is also 12 joules.


Electricity Exercise 6

Solution 16

(a) Potential difference between two points in an electric circuit is defined as the amount of work done in moving a unit charge from one
point to the other point.

(b) The potential difference between two points is 1 volt means 1 joule of work is done in moving 1 coulomb of electric charge from one point to the other. 

(c) Given: Work done = 250J, Charge moved = 20C

We know that,

                                                 

 

(d) A voltmeter is a device which is used to measure the potential difference between two points in an electric circuit. Voltmeter is always connected in parallel across the two points where the potential difference is to be measured.

 


(e) Voltmeter has a high resistance so that it takes a negligible current from the circuit. 

Solution 22

 

(a) If three cells of 2 volt each are connected in series to make a battery, then the total potential difference between terminals of the battery will be 6V.

(b) (i) Given: p.d. = 2V, Charge moved = 1C

              We know that

            

Work done = p.d. x charge moved

                = 2 x 1

Work done = 2 joules

          (ii) Given: p.d. = 6V, Charge moved = 1C

Work done = p.d. x charge moved

                 = 6 x1

Work done = 6 joule

Solution 23

Copper has free electrons that are loosely held by the nuclei of the atoms. These free electrons result in conduction of electricity.

The electrons present in rubber are strongly held by the nuclei of its atoms. So, rubber does not have free electrons to conduct electricity.

Electricity Exercise 11

Solution 1

Ampere

Solution 2

Electric Current

Solution 3

Electrons

Solution 4

Electrons

Solution 5

(a) Conventional current flows from positive terminal of a battery to the negative terminal, through the outer circuit.

(b) Electrons flow from negative terminal to positive terminal of the battery (opposite to the direction of conventional current).

Solution 6

1A = 1C/s

Solution 7

Ampere

Solution 8

(a) 1 amp = 103 milli amp

(b) 1 amp = 106 micro amp

Solution 9

Ammeter is connected in series.

Solution 10

Ammeter is connected in series in a circuit whereas voltmeter is connected in parallel.

Solution 11

(i) Variable resistance

(ii) A closed plug key

Solution 12

Given, Q = 20 C, t=1s

I=?

We know that:

 

Solution 13

Given I=4amp, t=10s
Q=?

We know that:

 

Solution 14

Given, Q=20C, t=40s

I=?

We know that:

 

Solution 15

(a) electrons; closed

(b) amperes; ammeter; series

Solution 16

(a) Cell or battery helps to maintain potential difference across a conductor. 

(b) Given: p.d. = 10 V, I = 2amp, t = 1 min = 60s 

We know that:-

Solution 17

(a) An electric currrent is a flow of electric charges (electrons) through a conductor.

Potential difference between the ends of the wire makes electric current to flow in the wire.

(b) When 1 coulomb of charge flows through any cross-section of a conductor in 1 second, the electric current flowing through it is said to be 1 ampere.

Solution 18

Ammeter is a device used for the measurement of electric current. It is always connected in series with the circuit in which the current is to be measured.

 

Solution 19

(b) I = 0.36 A, t = 15 min = 900 s

Solution 20

(a) The resistance of an ammeter should be very small so that it may not change the value of the current flowing in the circuit.

(b) The resistance of a voltmeter should be very large so that it takes a negligible current from the current.

Solution 21

Solution 22

A diagram which indicates how different components in a circuit have been connected by using the electrical symbols for the components is called a circuit diagram.

 

 

A voltmeter has a large resistance.

Solution 23

We know that


Now,

When charge is coulombs, number of electrons = 1

When charge is 1 coulomb, number of electrons =

 

Solution 24

Electricity Exercise 12

Solution 25

Solution 26

(a) Electric current is the flow of electric charges (electrons) in a conductor such as a metal wire.

SI unit of electric current is ampere.

(b) 1 ampere.

(c) An ammeter is used to measure electric current. It should be connected in series with the circuit.

(d) Conventional direction of flow of electric current is from positive terminal of a battery to the negative terminal, through the outer circuit. The direction of flow of electrons is opposite to the direction of conventional current, i.e. from negative terminal to positive terminal.



Solution 32

(a) Lamps are in series.

(b) Student has connected ammeter in parallel with lamps. It should be connected in series.

(c)


 

Solution 33

 

Solution 34

Solution 35

Electricity Exercise 18

Solution 1

Ohm's law

Solution 2

Solution 3

Electric resistance.

Solution 4

Insulators

Solution 5

Solution 6

Strength of electric current flowing in a given conductor depends on

(i) potential difference across the ends of the conductor

(ii) resistance of the conductor

Solution 7

Thick wire

Solution 8

Solution 9

Potential difference, V = 20V

Resistance, R = 5ohms

Current, I = ?

We know that

V=IR

20 = I x 5

I = 20/5 = 4 A

Solution 10

 R = 20ohms

I = 2amp

We know that

V = IR

Thus,

V = 2 x 20

V = 40V

Solution 11

 I = 5amp

p.d., V = 3V

We know that

V=IR

Thus,

3 = 5 x R

R = 3/5 = 0.6 ohm

Solution 12

current

Solution 13

Those substances which have very low electrical resistance are called as good conductors. E.g., copper and aluminium.

Those substances which have comparatively high resistance than conductors are known as resistors. E.g., nichrome and manganin.

Those substances which have infinitely high electrical resistance are called insulators. E.g., rubber and wood.

Solution 14

Conductor :- mercury, aluminum, iron, metal coin

Resistor :- manganin, nichrome

Insulator :- rubber, polythene, wood, bakelite, paper, thermocol

Electricity Exercise 19

Solution 15

Ohm's law gives a relationship between current (I) and potential difference (V). According to ohm's law: At constant temperature, the current flowing through a conductor is directly proportional to the potential difference across its ends.

If I is the current flowing through a conductor and V is the p.d. across its ends, then according to the ohm's law:

Solution 16

(a) The property of a conductor due to which it opposes the flow of current through it is called resistance of the conductor.

     

 


(b) V = 12volt, I=2.5 x 10-3 A

We know that

V=IR

R=V/I

R=12/(2.5X10-3)

R=4.8X103ohm = 4800 ohm

Solution 17

(a) 1 ohm is the resistance of a conductor such that when a potential difference of 1 volt is applied to its ends, a current of 1ampere flows through it.


(b) Its resistance will increase.


(c)

Solution 18

(a) Electricians wear rubber hand gloves while working with electricity because rubber is an insulator and protects them from electric shocks.

(b)  I=6amp, R=40ohm

We know that

V=IR

V = 6 x 40 = 240 V

Solution 19

(i)


(ii) Since the graph is a straight line passing through the origin, so current is directly proportional to the potential difference.

Hence, the ration  remains constant.

From graph, when V=1.5 volt, I=0.6 amp

So, =

For p.d. 0.8V, 1.2v and 1.6V, the value of ratio remains the same i.e., 2.5 ohm.

(iii) The resistance of the wire is equal to the ratio of potential difference applied and the current passing through it.

Solution 20

(a) The ratio of potential difference and current is known as resistance.

(b)

(c) Ohm's law

(d) Potential difference = Current x Resistane

(e)  V = 240 volt, I = 5amp 

We know that

V=IR

240 = 5 x R

R = 240/5 = 48 ohm

Electricity Exercise 20

Solution 30

In first case,

I = 2.4 amp, V = 120 volt 

V=IR

120 = 2.4 x R

R = 120/2.4 = 50 ohm


In second case,

V = 240 volt, R = 50 ohm

V = IR

240 = I x 50

I =4.8 amp

 

Solution 31

Resistance.

Solution 32

(a) Ohm's law

(b)  Temperature

Solution 33

In first case,

I = 0.02 amp, V = 10 volt 

V=IR

10 = 0.02 x R

R = 10/0.02 = 500 ohm

 

In second case,

I = 250 x 10-3 amp, R = 500 ohm

V = IR

V = 250 x 10-3 x 500

V = 125 volt

Solution 34

I = 200mA = 0.2 A

R = 4 x 103ohm = 4000 ohm 

We know that

V=IR

V = 0.2 x 4000

V = 800 volt

Electricity Exercise 26

Solution 1

The resistance decreases.

Solution 2

Resistance also gets doubled.

Solution 3

Resistance of a conductor depends on the following factors:-

Length of the conductor, area of cross section of the conductor, nature of material of the conductor and temperature of the conductor

Solution 4

Silver metal

Solution 5

Iron

Solution 6

Because copper and aluminium have very low resistivities.

Solution 7

Nichrome

Solution 8

Nichrome is an alloy of nickel, chromium, manganese ad iron having a resistivity of about 60 times more than that of copper. It is used for making the heating elements of electrical heating appliances.

Solution 9

Nichrome alloy is used for making the heating elements of electrical appliances because:

(i) nichrome has very high resistivity

(ii) nichrome does not undergo oxidation (or burn) easily even at high temperature.

Solution 10

Because

(i) resistivity of an alloy is much higher than that of a pure metal

(ii) an alloy does not undergo oxidation (or burn) easily even at high temperature.

Solution 11

(a) A long piece of nichrome wire.

(b) A thin piece of nichrome wire.

Solution 12

(a) On decreasing the temperature, the resistance decreases.

(b) Presence of impurities in a metal increases the resistance.

Solution 13

Ohms; increases; increases; decreases.

Solution 14

(a) Resistivity is the characteristic property of a substance which depends on the nature of the substance and its temperature. It is numerically equal to the resistance between the opposite faces of a 1 m cube of the substance.

      (b) l = 1m

            r = d/2 = 0.2/2 mm = 0.1 mm = 0.0001m,

           R = 10 ohm

           We know that,

          

Solution 15

 

Solution 16

(a) Silver and copper are good conductors of electricity because they have free electrons available for conduction.

 

Solution 17

Current will flow more easily through thick wire because the resistance of the thick wire will be lesser than that of thin wire.

Solution 18

(a) Resistance of a conductor increases (or decreases) with increase (or decrease) in the length of the conductor.

(b) Resistance of a conductor decreases (increases) with increase (decrease) in the area of cross-section of the conductor.

(c) Resistance of a conductor increases on raising the temperature and decreases on lowering the temperature.

 

Solution 19

(a) If we take two similar wires of same length and same diameter, one of copper metal and other of nichrome alloy, we will find that the resistance of nichrome wire is about 60 times more than that of the copper wire. This shows that the resistance depends on the nature of material of the conductor.


    

Solution 20

(a) Resistance will increase.

(b) Resistance will decrease.

(c) Resistance will increase.

Solution 21

(a) By increasing the area of cross section, the resistance will decrease.

(b) By increasing the diameter, the resistance will decrease.

Electricity Exercise 27

Solution 22

Solution 23

Solution 24

 

(b) Ohm-meter


(c) 1. Resistance is the property of the conductor, while resistivity is the property of the material of the conductor.

    2. Resistance of a conductor is the opposition to the flow of electric current through it. Resistivity of a substance is the opposition to the flow of electric current by a rod of that substance which is 1m long and 1m2 in cross section.

    3. Resistance of a conductor depends on length, thickness, nature of material and temperature of the conductor; while resistivity of a substance depends on the nature of the substance and temperature.


(d) Resistivity of a substance depends on the nature of the substance and its temperature. It does not depend on the length or thickness of the conductor.


    

Solution 33

Solution 34

(a) Material Q with resistivity 2.63 X 10-8 ohm-m can be used for making electric wires because it has very low resistivity.

(b) Material R with resistivity 1.0 X 1015 ohm-m can be used for making handle of soldering iron because it has very high resistivity.

(c) Material P with resistivity 2.3 X 103 ohm-m can be used for making solar cell because it is a semiconductor.

Solution 35

(a) Good conductor = C (10 x 10-8ohm-m)

(b) Resistor = A (110 x 10-8 ohm-m)

(c) Insulator= B (1 x 1010 ohm-m)

(d) Semiconductor= D (2.3 x 103 ohm-m)

 

Solution 36

(a) E is best conductor of electricity due to its least electrical resistivity.

(b) C, because its resistivity is lesser than that of A.

(c) B, because it has the highest electrical resistivity.

(d) C and E, because of their low electrical resistivities.

 

Electricity Exercise 37

Solution 1

According to the law of combination of resistances in series, the combined resistance of any number of resistances connected in series is equal to the sum of the individual resistances.

Solution 2

As per the law of combination of resistances in series,

R=R1+ R2+ R3+ R4+ R5

R=0.2+0.2+0.2+0.2+0.2=1ohm

Solution 3

According to the law of combination of resistance in parallel, the reciprocal of the combined resistance of a number of resistances connected in parallel is equal to the sum of the reciprocals of all the individual resistances.

Solution 4

Solution 5

Since the resultant resistance is less than the individual resistances, so the resistances should be connected in parallel.

Solution 6

In case of parallel combination, the resultant resistance will be less than either of the individual resistances.

Solution 7

R1=2ohm, R2=6ohm

Case I: (Parallel combination)

1/R = 1/R1+ 1/R2

1/R = 1/2 + 1/6 = 4/6

R = 6/4 = 1.5ohm

Case II: (Series combination)

R = R1 + R2 = 2+6 = 8ohm

Electricity Exercise 38

Solution 17

Solution 8

(a) By connecting in parallel: Since equivalent resistance will be

1/ R = 1/4 + 1/4 = 2/4 = 1/2

Therefore, R = 2 ohm

(b) By connecting in series : Since equivalent resistance will be

R = 4 ohm + 4 ohm = 8 ohm

Solution 9

Resistance of arrangement A is 10 ohm.

Combined resistance of arrangement B is caculated as follows:

1/R = 1/10 + 1/1000 = (100+1)/1000

R = 1000/101 = 9.9 ohm


Therefore, arrangement B has lower combined resistance.

Solution 10

Resistance of each part is R/2.

Resultant resistance R' is given by

1/R' = 2/R+2/R

R'=R/4

Solution 11

(a) R1=500ohm, R2=1000ohm

As per given figure,

R=R1+R2=500+1000=1500ohm.

(b) R1=2ohm, R2=2ohm

As per given figure,

1/R=1/R1+1/R2

1/R=1/2+1/2

R=1ohm

(c) R1=4ohm, R2=4ohm, R3=3ohm

As per given figure,

1/R=1/R1+1/R2

1/R=1/4+1/4

R=2ohm

Total resistance =R+R3

=2+3=5ohm

Solution 12

R1=6ohm, R2=4ohm V=24V

The two resistances are connected in parallel.

Current across R1=I1=V/R1=24/6=4amp

Current across R2=I2=V/R2=24/4=6amp

Solution 13

(i) Series combination

When two or more resistances are connected end to end consecutively, they are said to be connected in series combination. The combined resistance of any number of resistances connected in series in equal to the sum of the individual resistances.

R=R1+R2+......

 

The resultant resistance is more than either of the individual resistances.

 

(ii) Parallel combination

When two or more resistances are connected between the same two points, they are said to be connected in parallel combination. The reciprocal of the combined resistance of a number of resistances connected in parallel is equal to the sum of the reciprocals of all the individual resistances.


1/R=1/R1+1/R2+........

       

The resultant resistance is less than either of the individual resistances.

Solution 14

R1=0.2ohm, R2=0.4ohm, R3=0.3ohm, R4=0.5ohm, R5=12ohm, V=9V

Resultant resistance=R1+ R2+ R3+ R4+ R5

R=0.2+0.4+0.3+0.5+12=13.4ohm

Thus the current flow through 12ohm resistance will be=V/R

I=9/13.4

I=0.67amp.

Solution 15

 

(a) Total resistance of the circuit=R1+R2=20+4=24ohm

(b) We know that

V=IR

Therefore,

6=I x 24

I=6/24=0.25amp

(c) p.d. across bulb=IR1=0.25X20=5V

(d) p.d. across resistance wire=IR2=0.25X4=1V


Solution 16

      According to the diagram,

(i) Total current I=1amp is entering the parallel combination of R1 and R2. Let I1 current flow through R1 and I2 current flow through R2.

Then

 

(ii) p.d. across AB = IR3 = 1 x 5 = 5V

Equivalent resisyance between B and C is

1/R' = 1/R1 + 1/R2 = 1/10 + 1/15

1/R' = 5/30

R' = 6 ohm

Total resistance between A and C is R = 5+6 = 11 ohm

p.d. across AC = IR = 1x11 = 11V


     (iii) Total resistance = R3 + R' = 5 + 6 = 11 ohm

Electricity Exercise 39

Solution 18

Given: Two resistors with resistances R1=5ohm and R2=10ohm, V=6volt

(a) For minimum current these two should be connected in series. For maximum current these two should be connected in parallel.

(b)In series,

Total resistance = 5+10 = 15ohms

Therefore total current drawn = V/R = 6/15 = 0.4amps

In parallel,

Total resistance R is given as

1/R=1/R1+1/R2

1/R=1/5+1/10

1/R=3/10

R=10/3ohm

Therefore total current drawn by the circuit = V/R = 6/(10/3) =1.8amps

Solution 19

 (i) Total resistance of two resistors that are connected in parallel is

1/R' = 1/3+1/6

1/R' = 3/6

R' = 2ohms

Total resistance of the circuit = 2+4ohms = 6ohms

 

(ii) Total current flowing through the circuit=V/total resistance

I = 12/6 = 2amps

 

(iii) Potential difference across R1=R1 x I = 4 x 2 = 8V

Solution 20

Given :-

1 amp current is flowing through 5ohm resistor.

We know that in case of parallel connection, the p.d. across each resistor is same and is equal to the voltage applied.

Therefore, applied voltage, V = IR = 1 x 5 = 5V

So,

Current through 4 ohm resistor = V/R = 5/4 = 1.25 A

Current through 10 ohm resistor = V/R = 5/10 = 0.5 A

Solution 21

Solution 22

Given V=220V

RA = RB = 24 ohm

(a) Current drawn when only coil A is used:

I = V/RA = 220/24

             =9.16amps

(b) Current drawn when coils A and B are used in series:

Total resistance, R = RA + RB = 24+24 = 48ohms

 I = V/R = 220/48

             =4.58amps

(c) Current drawn when coils A and B are used in parallel:

Total resistance, 1/R = 1/RA + 1/RB = 1/24 + 1/24 = 2/24 = 1/12

R=12ohms

I = V/R = 220/12

           =18.33amps

Solution 23

Electricity Exercise 40

Solution 24

V=12V

R1, R2 and R3  are connected in parallel.


(a) Current through R1 = V/R1 = 12/5 = 2.4 A

     Current through R2 = V/R2 = 12/10 = 1.2 A

     Current through R3 = V/R2 = 12/30 = 0.4 A

 

(b) Total current in the circuit = 2.4 + 1.2 + 0.4 = 4 A

 

(c)  Total resistance in the circuit=R

                
     1/R = 1/R1+ 1/R2 + 1/R3

     1/R = 1/5 + 1/10 + 1/30            

     1/R = 10/30

     R = 3 ohm

Solution 25

V = 4V, 

R1 = 6 ohm, R2 = 8 ohm (in series)

(a) Combined resistance, R = R1 + R2 = 6+2 = 8ohm

(b) Current flowing, I = V/R = 4/8=0.5amp

 

(c) p.d. across 6ohm resistor = I x R1 = 0.5 x 6 = 3 V

 

Solution 26

V = 6V

R1 = 3 ohm, R2 = 6 ohm (in parallel)

(a) Combined resistance,

1/R = 1/R1 + 1/R2

1/R = 1/3 + 1/6 = 3/6 = 1/2

R = 2 ohm

(b) Current flowing in the main circuit, I = V/R = 6/2 = 3 A

(c) Current flowing in 3 ohm resistor = V/R1 = 6/3 = 2 A

Solution 28

Total current flowing through circuit, I = 6 A

R1 = 3 ohm, R2 = 6 ohm

(a) Combined resistance R is

1/R=1/3+1/6

1/R=3/6

R=2ohms

(b) p.d. across the combined resistance = IR = 6 x 2 = 12 V

(c) p.d. across the 3 ohm resistor = p.d. across the combined resistance = 12 V

(d) Current flowing through the 3 ohm resistor = V/R1 = 12/3 = 4 A

(e) Current flowing through the 6 ohm resistor = V/R2 = 12/6 = 2 A

Solution 27

Electricity Exercise 41

Solution 29

      (a)
        

 

(b) Effective resistance = 20 + 20 = 40 ohms


(c) Current flowing through the circuit = I = V/R = 5/40 = 0.125 amps


(d) p.d. across each resistance = I x R = 0.125 x 20 = 2.5 V

Solution 30

V=6V, R1=2ohms, R2=3ohms

(a) Resistors are connected in parallel

(b) p.d. across each resistor is same and is equal to 6V.

(c) 2 ohms resistance have bigger share of current because of its lower resistance.

(d) Effective resistance=R

     1/R=1/2+1/3

     1/R=5/6

     R=1.2ohms

(e) Current flowing through battery, I=V/R=6/1.2=5amps

Solution 33



Solution 31

Solution 32

Electricity Exercise 42

Solution 34

(a)


Suppose total current flowing the circuit is I, then the current passing through resistance R1 will be I1 and current passing through resistance R2 will be I2.

Total current =I=I1+I2

Let resultant resistance of this parallel combination is R. By applying the Ohm's law to the whole circuit, we get that I=V/R

Since the potential difference across the both the resistances is same, so applying the Ohm's law to each resistance we get that

I1=V/R1

I2=V/R2

Putting these eq in the above one, we get that

V/R=V/R1+V/R2

1/R=1/R1+1/R2

If two resistance are connected in parallel than, the resultant resistance will be

1/R=1/R1+1/R2

(b)

(i) Total reisitance=R

1/R=1/R1+1/R2

R2=3+2=5ohms

R1=5ohms

1/R=1/5+1/5

1/R=2/5

R=2.5ohms

(ii) Current flowing through the circuit

I=V/R=4/(2.5)

=1.6amps


Solution 35

(a)


Suppose total current flowing in the circuit is I, then the current passing through resistance R1 will be I1, current passing through resistance R2 will be I2 and current passing through resistance R3 will be I3.

Total current =I=I1+I2+I3

Let resultant resistance of this parallel combination is R. By applying the Ohm's law to the whole circuit, we get that

I=V/R

Since the potential difference across all the resistances is same, so applying the Ohm's law to each resistance we get that

I1=V/R1

I2=V/R2

I3=V/R3

Putting these eqs. in the above one, we get

V/R=V/R1+V/R2+ V/R3

1/R=1/R1+1/R2+ 1/R3

If two resistance are connected in parallel, then the resultant resistance will be

1/R=1/R1+1/R2+ 1/R3

 

(b) If switch is open, then only upper two resistances (connected in parallel) are in the circuit.

Effective resistance is 1/Req=1/R+1/R=2/R            
Req = R/2

So the current=I=V/(R/2)=0.6A (given)

V/R = 0.3 A

When the switch closes, the third resistance also comes in the circuit. The effective resistance of the circuit becomes R/3

Hence, Current I = V/(R/3) = 3 (V/R) = 3 x 0.3 = 0.9 A

Electricity Exercise 43

Solution 43

(i)

 

Resultant resistance for parallel circuit=R

1/R=1/6+1/6

1/R=2/6

R=3

Effective resistance=6+3=9ohms

(ii)

 

 

Resultant resistance for each parallel circuit=R

1/R=1/6+1/6+1/6

1/R=3/6

R=2

Therefore effective resistance=2+2=4ohms.


Solution 44

Two resistances when connected in series, resultant value is 9ohms.

Two resistances when connected in parallel, resultant value is 2ohms.

Let the two resistances be R1 and R2.

If connected in series, then

9=R1+R2

R1=9-R2

If connected in parallel, then

1/2=1/R1+1/R2

From above equations we get that

1/2=(R1+R2)/R1R2

 1/2=9/(9-R2) R2

9R2-R22=18

R22-9R2+18=0

(R2-6) (R2-3)=0

R2=6,3

So if R2=6ohms, then R1=9-6=3ohms.

If R2=3ohms, then R1=9-3=6ohms.


Solution 45

Given:

A resistor of 8ohm is connected in parallel with a resistor of X.

And resultant is 4.8.

Then X=?

We know that for parallel case

1/R=1/R1+1/X

1/4.8=1/8+1/x

1/4.8 - 1/8 = 1/x

After solving we get that

X=12ohms

Solution 46


Electricity Exercise 44

Solution 47

Given: Three resistances of 2ohms, 3ohms, 5ohms.

Their resultant, R=2.5ohms

Resistance of first line = 2+3 = 5 ohm

So, 1/R = 1/5 + 1/5

On solving we get that

R=2.5ohms

Solution 48

(a) Connect 2ohms resistor in series with a parallel combination of 3ohms and 6ohms.

(b) Connect 2ohms, 3ohms, and 6ohms in parallel.

Solution 49

(a) For obtaining the highest resistance by combining the given resistances, we must connect them in series.

We get,

R=4+8+12+24=48ohms

(b) For obtaining the lowest resistance by combining the given resistances, we must connect them in parallel.

We get,

1/R=1/4+1/8+1/12+1/24

On solving we get, R=2ohms

Solution 50

The three resistance of 20 ohm, 10 ohm and 20 ohm on the extreme right side are in series.

So, the resultant of these three resistances = 20+20+10 = 50ohms.

This 50ohms is in parallel with 30ohms. So resultant of these two will be

1/R=1/30+1/50

1/R=80/1500

R=18.75ohms

Now, the resistances 10 ohms, 18.75 ohms and 10 ohms are in series.

Therefore, resultant resistance = 18.75+10+10 = 38.75ohms.

Solution 51

Given: n=100, R=1 ohm

For obtaining the smallest resistance, these resistances are connected in parallel:

Equivalent resistance = 1/1 + 1/1 + 1/1.....100 times = 100/1

Req = 1/100 = 0.01 ohm

For obtaining the largest resistance, these resistances are connected in series:

Equivalent resistance = 1 + 1 + 1.....100 times = 100

Req = 100 ohm

Solution 52

For obtaining 250ohms, connect two 100ohms in series with a parallel combination of two 100ohms.

Solution 53

Req = R+R+R+R = 4R ohm

Total current in the circuit, I = V/R = 12/4R = 3/R

Reading of voltmeter A = Voltage across R1 = I x R1 = 3/R x R = 3V

Reading of voltmeter B= Voltage across R2 = I x R2 = 3/R x R = 3V

Reading of voltmeter C= Voltage across the series combination of R3 and R4 = I x (R3+R4) = 3/R x 2R = 6V


Solution 54

Resultant resistance of a parallel combination of four 16 ohm resistances is

1/R = 1/16 + 1/16 + 1/16 + 1/16 = 4/16

R = 4 ohm

Four such combinations are connected in series, so total resistance = 4+4+4+4 = 16 ohm.

Exercise

Solution

Electricity Exercise 47

Solution 6

A series arrangement is not used for connecting domestic electrical appliances in a circuit because if one electrical appliance stops working due to some defect, then all other appliance also stop working as the whole circuit is broken.

Solution 7

Different electrical appliances in a domestic circuit are connected in parallel because of the following advantages:

(i) If one electrical appliance stops working due to some defect, then all other appliances keep working properly.

(ii) Each electrical appliance has its own switch due to which it can be turned on or turned off independently, without affecting other appliances.

(iii) Each electrical appliance gets the same voltage as that of the power supply line.

Solution 8

(a) Parallel circuit

(b) Parallel circuit

(c) Series circuit

(d) Series circuit.

Solution 9

(a) circuit (ii)

(b) circuit (iii)

(c) circuit (iii) 

Solution 1

No, they are wired in parallel.

Solution 2

All the other bulbs also stop glowing.

Solution 3

All the other bulbs keep glowing.

Solution 4

(a) Series

(b) Parallel

Solution 5

 

The two lamps (of 4V each) should be arranged in parallel with the two 2V cells.

Electricity Exercise 48

Solution 10

Parallel arrangement because if one electrical bulb stops glowing due to some defect the other will keep glowing.

Parallel arrangement takes more current from the battery due to its lesser equivalent resistance.

Solution 11

(a) Parallel circuits - Because if one electrical appliance stops working due to some defect, then all other appliances in the circuit will keep working properly.


(b)  All the other lamps stop glowing.


(c) All lamps are connected in series.


(d)

 

Solution 14

(a)


 

(b) The brightness of the lamps can be changed by connecting the lamps in parallel.

Solution 15

(a) C will be the brightest. Voltage will be distributed equally between A and B, so they will have equal brightness but lesser than that of C.

(b) A gets the same voltage as before, so its brightness remains the same.

(c)  If B burns put, A will also stop glowing because it is connected in series with B. However, brightness of C remains the same.

Solution 16

The brightness of two lamps arranged in parallel is much more those arranged in series.

Solution 17

(a) In case of series connection, if filament of one lamp breaks, the other wil stop glowing.

(b) In case of parallel connection, if filament of one lamp breaks, the other will keep glowing.

Electricity Exercise 49

Solution 18

(a) Turn the switch to right side so as the resistance decreases.

(b) Turn the switch to the left side so as the resistace increases.

Electricity Exercise 58

Solution 1

Electrical energy consumed by an electrical appliance depends on:

1. Power rating of the appliance.

2. Time for which the appliance is used.

Solution 2

60 watt bulb, because power is inversely proportional to the resistance.

Solution 3

Kilowatt-hour is the commercial unit of electric energy.

Solution 4

V = 220 V, P = 100W

R=?

We know that

P = V2/R

Thus

R = V2/P = 2202/100 = 484ohm

Solution 5

(i) joule

(ii) watt

Solution 6

(i) Electric power

(ii) Electric energy

Solution 7

Electric power has the unit of watt.

Solution 8

kWh is the short form of kilowatt-hour, which is the commercial unit of electrical energy.

Solution 9

P=V2/R

R is fixed.

V becomes double.

Now, P = (2V)2/R = 4 V2/R

 So, the electric power becomes four times its previous value.

Solution 10

Other information is that it will consume energy at the rate of 36 J/s.

Solution 11

P=920W, V=230V, I=?

We know that

P = V x I,

920 = 230 x I

I = 920/230 = 4amp

Solution 12

When an electrical appliance consumes electrical energy at the rate of 1 joule per second, its power is said to be 1 watt.

1 watt = 1 volt x 1 ampere

Solution 13

One watt hour is the amount of electrical energy consumed when an electrical appliance of 1 watt power is used for 1 hour.

1 watt hour = 3600 joules

Solution 14

I=5amp, R=100ohms, t=2h

We know that

Electric energy consumed = P x t = I2Rt

                                   = 52 x 100 x 2

                                   = 5000 Wh

                                   = 5 kwh

We know that 1kwh = 3.6 x 106 J

Therefore, 5kwh = 5 x 3.6 x 106 J = 18 x 106 J

Solution 15

V=220V, I=0.5amp, P=?

We know that

P=VI=220X0.5

P=110 watt

Solution 16

(i) R = 300 ohm, I = 1 A, t = 1h

P = I2R = 12 x 300 = 300 W

E = P x t = 300 x 1 = 300 Wh


(ii) R = 100 ohm, I = 2 A, t = 1h

P = I2R = 22 x 100 = 400 W
E = P x t = 400 x 1 = 400 Wh


Hence, in case (ii), the electrical energy consumed per hour is more.

Solution 17

V=220V, P=2.2kW=2200W, t=3h

We know that

Electrical energy consumed = Pxt = 2.2x3 = 6.6 kWh


We have, P = V x I

2200 = 220 x I

I=10amp

Electricity Exercise 59

Solution 18

Solution 19

V=250V, I=0.4amp


(i) We know that


Power=VI=250X0.4=100watt

      (ii) We have

      P=I2R

      100=0.42XR

      R=625ohm

Solution 21

I=5amp, V=220volt, t=2h

P=?, E=?

P=VXI

  =220X5

  =1100watt

  =1.1kW

Energy consumed, E=PXt

                            =1.1X2

                            =2.2kWh

Solution 22

Case 1: TV set

P=250W=0.25kWh

t=1h

Energy consumed=PXt=0.25X1=0.25kWh


Case 2: Toaster

P=1200W=1.2kW, t=10min=10/60=1/6h

Energy consumed=PXt=1.2X(1/6)=0.2kWh


Thus, TV uses more energy.

Solution 23

Solution 24

Given 2 lamps:P1=40W, P2=60W


V=220V


(a)

 

(b) Voltage across both the bulbs is same and is equal to 220V.

Current through 40W lamp = I1 = P1/V = 40/220 A

Current through 60W lamp = I2 = P2/V = 60/220 A

Total current drawn from the electric supply = 40/220 + 60/220 = 0.45 A


(a) Energy consumed by 40 W lamp in 1 hr, E1 = P1 x t = 40 x 1 = 40Wh 

1Wh = 3.6 kJ

E1 = 40 x 3.6 = 144 kJ

Energy consumed by 60W lamp in 1 hr, E2 = P2 x t = 60 x 1 = 60Wh = 216 kJ

Total energy consumed = 144 + 216 = 360 kJ


Solution 25

Given V=230V, I=10amp

(a) P=VI

P=230X10

P=2300watt = 2300 J/s

(b) Energy consumed in minute = P x t = 2300 J/s x 60s = 138000 J

 

Solution 26

For heater:

P=2kW, t=4h

E=Pxt=2x4=8kWh

For TV:

P=200W=0.2kW, t=4h

E=Pxt=0.2x4=0.8kWh

Lamps:

P=100W=0.1kW, t=4h, n=3

E=nxPxt=3x0.1x4=1.2kWh

 

Total energy consumed = 8+0.8+1.2 = 10kWh

Cost of 1kWh = Rs. 5.50

Cost of 10kWh = Rs. 5.50 x 10 = Rs. 55

Solution 27

I=13amp, V=230V

Power=VI

        =230X13

        =2990W

P=2.99kW

Solution 28

Given :- V=230V, I=0.4amp

Rate at which electric energy is transferred = Power

Power = VxI

          = 230 x 0.4

          = 92 W = 92 J/s

Solution 29

(a) The rate at which electrical work is done or the rate at which electrical energy is consumed, is known as electric power.

It is given by

P=VI=watt

(b) Given: V=3V, I=0.5amp

(i) R=?

We know that V=IR 

3=0.5R

R=6ohms

(ii) Power of lamp=VI

                        =3x0.5

                        =1.5watt

(c) One kilowatt hour is the amount of electrical energy consumed when an electrical appliance having a power rating of 1 kilowatt is used for 1 hour.

1kWh=3.6x106J

(d) Given P=500W=0.5kW, t=20hr

We know that

Energy consumed =Pxt=0.5X20

                         =10kwh

Total cost =10xcost per uint

Cost per unit=Rs. 3.9 per unit

Therefore, total cost=10x3.9=Rs 39

Solution 20

Given

P=4kw, V=220v

(a) I=?

Power=VI=250XI

4000=250I

I=16amp

(b) R=?

P=I2R

P=162XR

R=4000/162

R=15.25ohm

 

(c) Energy consumed in two hour=PXt

=4X2

=8kw-hr

(d) If 1kwh=Rs 4.6

total cost=8 x 4.6=Rs 36.8

Electricity Exercise 60

Solution 41

By reducing the length of element the resistance will decrease.

Power is inversely proportional to resistance. So, this will result in more consumption of energy.

Solution 42

(a) Lamp; because least current is flowing through it.

(b) Large current drawn by the kettle; Earth connection needed.

(c) We know that

P=VI

V=240V, I=8.5A

P=240X8.5=2040W=2.04kW

(d) When connected to 240 V supply, P=2040W

R = V2/P = 2402/240

R=28.23ohm

Now, when V=120V, R=28.23ohm

I=V/R=120/28.23=4.25A

Solution 43

(a) 42919

(b) 42935

(c) 42935-42919=16 units

(d) 24 hours

(e) Cost of 1 unit = Rs. 5

Cost of 16 units = 16x5 = Rs. 80

Solution 44

P=10W, V=220V, I=5A

We know that

P=VI

=220X5

P=1100W

Power of one bulb=10W

Total no. of bulbs that can be connected=1100/10=110

Solution 45

Electricity Exercise 66

Solution 1

Heat produced is directly proportional to the square of current.

Solution 2

If current I is doubled, heat H will be four times.

Solution 3

Two effects of produced by electric current are:

(a) Heating effect

(b) Magnectic effect

Solution 4

Heating effect

Solution 5

Heating effect

Solution 6

Electirc heater and electric fuse.

Solution 7

Argon and nitrogen.

Solution 8

Filament type electric bulbs are not power efficien because most of the electric power consumed by the filament of a bulb appears as heat and only a small amount of electric power is converted into light.

Solution 9

The connecting cord of the heater made of copper does not glow because negligible heat is produced in it by passing current (because of its extremely low resistance); but the heating element made of nichrome glows because it becomes red-hot due to the large amount of heat produced on passing current (because of its high resistance).

Solution 10

(a) Heat produced, H=I2Rt

(b) Given: R=20ohm, I=5amp, t=30s

We know that H=I2Rt

H=52x20x30

H=15000 J

Solution 11

Heat produced by an electric current depends on the following factors:

(i) Heat produced is directly proportional to square of current.

(ii) Heat produced is directly proportional to resistance.

(iii) Heat produced is directly proportional to the time for which current flows.

 

Solution 12

(a) Joule's law of heating states that heat produced in joules when a current of I amperes flows in a wire of resistance R ohms for time t seconds is given by H = I2Rt.

Thus the heat produced in a wire is directly proportional to:

(i) Square of current

(ii) Resistance of wire

(iii) Time for which current is passed

(b)  Given: R1=40ohms, R2=60ohms (in series), V=220V, t=30sec

We know that

Total resistance, R=40+60=100ohms

By Ohm's law,

V=IR

I=V/R

I=220/100=2.2amp

Putting the values of I, R and t in eq.  H=I2RT

H= 2.22  X  100  X  30

H= 14520 J

Solution 13

If air is filled in an electric bulb, then the extremely hot tungsten filament would burn up quickly in the oxygen of air. So, the electric bulb is filled with a chemically unreactive gas like argon or nitrogen. Thes gases do not react with the hot tungsten filament and hence prolong the life of the filament of the bulb.

Solution 14

Tungsten is used for making the filaments of electric bulbs because it has a very high melting point. Due to its very high melting point, the tungsten filament can be kept white hot without melting away. Also, tungsten has  high flexibility and low rate of evaporation at high temperature.

Solution 15

The connecting wires of the heater get only slightly warm because they have extremely low resistance due to which negligible heat is produced in them by passing current.

Solution 16

Given: I=4amp, t=10min=10x60=600sec, H=2.88x104J

(a) We have

H=I2RT

28800=42xRx600

R=3ohms

We know that

P=I2xR

  =42x3

P =48W

(b) V=?

We know that

V=IR

V=4x3

V=12V

Solution 17

Given: R=200ohms, I=2.5amp, t=1sec

We know that

H=I2RT

H=2.52X200X1

H = 1250 J/s

Solution 18

Given: R=8ohms, I=15amp, t=1sec

We know that

H=I2RT

H=152X8X1

H=1800J/s

Solution 19

Given: R=25ohms, V=12V, H=?, t=60sec

V=IR

12=25XI

I=0.48amp

We have

H=I2RT

H=0.482X25X60

H=345.6J

Solution 20

Given: H=100J, t=1sec, R=4ohms,

We know that

H=I2RT

100=I2X4X1

100/4=I2

I=5amp

V=IR

V=5X4

  =20V

Solution 21

          

(b) Given: P=12W, V=12V, t=60sec

P=VI

I=P/V=12/12=1A

V=IR

R=V/I=12/1=12ohm

H=I2Rt 

H=12x12x60

H=720J

(c)  The heat produced by the heater will become one-fourth because heat produced is directly proportional to the square of the current.

(d) When an electric current is passed through a high resistance wire, the wire becomes very hot and produces heat. This effect is knows as heating effect of current. This effect is used in room heaters and electric ovens.

 (e) Tungsten is used for making the filaments of an electric bulb.

 

    

Electricity Exercise 67

Solution 31

(a) S; because it has high resistivity of 11X10-7ohm-m (it is actually nichrome).

(b) Q; because it has very low resistivity of 1.7 X10-8ohm-m (it is actually copper).

(c) R; because it has very very high resistivity of 1.0X1015ohm-m (it is actually rubber).

Solution 32

(a) The filament wire becomes white hot where as other wires in the circuit do not get heated much.

(b) High resistance of filament wire accounts for this difference.

Solution 33

In series, because total resistance in series connection is more than that in parallel connection.

Solution 34

Given: V=220V, Pmin=360W, Pmax=840W


For minimum heating case:

We know that

Pmin=VI

360=220XI

I=1.63amp

R=V/I

R=220/1.63

R=134.96ohms


For maximum heating case:

We know that

Pmax=VI

840=220XI

I=3.81amp

R=V/I

R=220/3.81

R=57.74ohms

Solution 35

Electric iron , electric oven, water heater, room heater.

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