H C VERMA Solutions for Class 12-science Physics Chapter 19 - Electric Current through Gases

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Chapter 19 - Electric Current through Gases Exercise 352

Question 1

A discharge tube contains helium at a low pressure. A large potential difference is applied across the tube. Consider a helium atom that has just been ionized due to the detachment of an atomic electron. Find the ratio of the distance travelled by the free electron to that by the free electron to that by the positive ion in a short time dt after the ionization.

Solution 1

Force is given as:

 H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

and  H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

 H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

For time period 'dt'

 H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Also,

 H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases (for positive ion)

 H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Taking ratio of (1) and (2), we get

 H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Question 2

A molecule of a gas, filled in a discharge tube, gets ionized when an electron is detached from it. An electric field of 5.0 kV/m exists in the vincinity of the event. (a) Find the distance travelled by the free electron in 1H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gasess assuming no collision. (b) If the mean free path of the electron is 1.0mm, estimate the time of transit of the free electron between successive collisions.

Solution 2

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

and H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

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

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

t=1.5ns

Chapter 19 - Electric Current through Gases Exercise 353

Question 3

The mean free path of electrons in the gas in a discharge tube is inversely proportional to the pressure inside it. The crookes dark space occupies half the length of the discharge tube when the pressure is 0.02mm of mercury. Estimate the pressure at which the dark space will fill the whole tube.

Solution 3

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

If P becomes half then L will double.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases Pressure required=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gasesm of Hg.

Question 4

Two discharge tubes have identical material structure and the same gas is filled in them. The length of one tube is 10cm and that of the other tube is 20cm. Sparking starts in both the tubes when the potential difference between the cathode and anode is 100V. If the pressure in the shorter tube is 1.0mm of mercury, what is the pressure in the longer tube?

Solution 4

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gasesmm

Question 5

Calculate n(T)/n(1000K) for tungsten emitter at T=300K, 2000K and 3000K where n(T) represents the number of thermions emitted per second by the surface at temperature T. Work function of tungsten is 4.52eV.

Solution 5

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

And

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

(a) If T=300K then,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

(b) If T=2000K then,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

(c) If T=3000K then,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Question 6

The saturation current from a thoriated-tungsten cathode at 2000K is 10mA. What will be the saturation current for pure-tungsten cathode of the same surface area operating at the same temperature? The constant A in the Richardson-Dushmaan equation is H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases for pure tungsten and H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases for thoriated tungsten. The work function of pure tungsten is 4.5eV and that of thoriated tungsten is 2.6eV.

Solution 6

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

For H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

For H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Dividing eq (1) and (2), we get

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through GasesA

Question 7

A tungsten cathode and a thoriated-tungsten cathode have same geometrical dimensions and are operated at the same temperature. The thoriated-tungsten cathode gives 5000 times more current than the other one. Find the operating temperature. Take relevant data from the previous problem.

Solution 7

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Also,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Taking log and solving we get,

T=2391.85K

Question 8

If the temperature of a tungsten filament is raised from 2000K to 2010K, by what factor does the emission current change? Work function of tungsten is 4.5eV.

Solution 8

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases and H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Dividing both equations above we get,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Question 9

The constant A in the Richardson-Dushman equation for tungstenH-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases. The work function of tungsten is 4.5eV. A tungsten cathode having a surface are H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases is heated by a 24W electric heater. In steady state, the heat radiated by the cathode equals the energy input by the heater and the temperature becomes constant. Assuming that the cathode radiates like a blackbody, calculate the saturation current due to thermions. Take Stefan constant=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases. Assume that the thermions take only a small fraction of the heat supplied.

Solution 9

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases [AS emissivity is 1]

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

T=2114.7K

Also,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through GasesmA

Question 10

A plate current of 10mA is obtained when 60volts are applied across a diode tube. Assuming the Langmuir-Child equation H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases to hold, find the dynamic resistance rp in this operating condition.

Solution 10

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Differentiating we get

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Now, dividing above equations we get,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases [H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases]

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through GaseskΩ 

Question 11

The plate current in a diode is 20mA when the plate voltage is 50V or 60V. What will be the current if the plate voltage is 70V?

Solution 11

Plate have voltage of 50V or 60V, so its acts as saturation current.

Hence, for other value of voltages current is 20mA.

Question 12

The power delivered in the plate circuit of a diode is 1.0W when the plate voltage is 36V. Find the power delivered if the plate voltage is increased to 49V. Assume Langmuir-Child equation to hold.

Solution 12

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases and H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Also,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Now,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through GasesW

Question 13

A triode value operates at Vp=225V and Vg= - 0.5V. The plate current remains unchanged if the plate voltage is increased to 250V and the grid voltage is decreased to -2.5V. Calculate the amplification factor.

Solution 13

Amplification factor is:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Question 14

Calculate the amplification factor of a triode value which has plate resistance of 2kΩ and trans conductance of 2 millimho.

Solution 14

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Question 15

The dynamic plate resistance of a triode value is 10kH-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases. Find the change in the plate current if the plate voltage is changed from 200V to 220V.

Solution 15

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through GasesmA

Question 16

Find the values of rp, μ and gm of a triode operating at plate voltage 200V and grid voltage -6V. The plate characteristics as shown in figure.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases

 

Solution 16

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

and H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Also, we know

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Question 17

The plate resistance of a triode is 8kH-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases and the transconductance is 2.5millimho. (a) If the plate voltage is increased by 48V, and the grid voltage is kept constant, what will be the increase in the plate current? (b) With plate voltage kept constant at this increased value, how much should the grid voltage be decreased in order to bring the plate current back to its initial value?

Solution 17

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

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

Question 18

The plate resistance and the amplification factor of a triode are 10 kΩ and 20. The tube is operated at plate voltage 250V and grid voltage -7.5V. The plate current is 10mA. (a) To what value should the grid voltage be changed so as to increase the plate current to 15mA? (b) To what value should the plate voltage be changed to take the plate current back to 10mA?

Solution 18

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

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases [As H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases]

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

And thus, grid voltage should be charged by,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

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

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through GasesV

or H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through GasesV

Question 19

The plate current, plate voltage and grid voltage of a 6F6 triode tube are related as

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Where vp and vg are in volts and ip in microamperes. The tube is operated at vp= 250v, vg=- 20v. Calculate (a) the tube current, (b) the plate resistance, (c) the mutual conductance and (d) the amplification factor.

Solution 19

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

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through GasesmA

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

Differentiating above equation we get

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Also, H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

(c) H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

(d) H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Question 20

The plate current in a triode can be written as

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Show that the mutual conductance is proportional to the cube root of the plate current.

Solution 20

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Differentiating we get,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Comparing (1) and (2) we get

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

or H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Question 21

A triode has mutual conductance=2.0 millimho and plate resistance=20kΩ. It is desired to amplify a signal by a factor of 30. What load resistance should be added in the circuit?

Solution 21

We know,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

RL = 60kΩ  

Chapter 19 - Electric Current through Gases Exercise 354

Question 22

The gain factor of an amplifier is increased from 10 to 12 as the load resistance is changed from 4 kΩ to 8 kΩ. Calculate (a) the amplification factor and (b) the plate resistance.

Solution 22

Voltage gain, H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Case 1: H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Case 2:H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Solving equation (1) and (2)

We get: H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

And H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Question 23

Figure shows two identical triode tubes connected in parallel. The anodes are connected together, the grids are connected together. Show that the equivalent plate resistance is half of the individual plate resistance, the equivalent mutual conductance is double the individual conductance and the equivalent amplification factor is the same as the individual amplification factor.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases

 

 

Solution 23

Resistances are connected in parallel, thus equivalent resistance is given as:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Also, equivalent conductance is given as:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Now,

Equivalent amplification is given as:

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Electric Current Through Gases 

Which is same as individual mutual conductance.