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

## Chapter 19 - Electric Current through Gases Exercise 352

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.

Force is given as:

and

For time period 'dt'

Also,

(for positive ion)

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

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 1s 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.

We know,

and

(a) m

(b)

t=1.5ns

## Chapter 19 - Electric Current through Gases Exercise 353

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.

We know,

If P becomes half then L will double.

Pressure required=m of Hg.

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?

We know,

mm

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.

And

(a) If T=300K then,

(b) If T=2000K then,

(c) If T=3000K then,

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 for pure tungsten and for thoriated tungsten. The work function of pure tungsten is 4.5eV and that of thoriated tungsten is 2.6eV.

We know,

For

For

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

A

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.

We know,

Also,

Taking log and solving we get,

T=2391.85K

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.

and

Dividing both equations above we get,

The constant A in the Richardson-Dushman equation for tungsten. The work function of tungsten is 4.5eV. A tungsten cathode having a surface are 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=. Assume that the thermions take only a small fraction of the heat supplied.

We know,

[AS emissivity is 1]

T=2114.7K

Also,

mA

A plate current of 10mA is obtained when 60volts are
applied across a diode tube. Assuming the Langmuir-Child equation to hold, find the
dynamic resistance r_{p} in this operating
condition.

We know,

Differentiating we get

Now, dividing above equations we get,

[]

kΩ

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?

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

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

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.

We know,

and

Also,

Now,

W

A triode value operates at V_{p}=225V
and V_{g}= - 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.

Amplification factor is:

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

We know,

The dynamic plate resistance of a triode value is 10k. Find the change in the plate current if the plate voltage is changed from 200V to 220V.

We know,

mA

Find the values of r_{p},
μ and g_{m} of a triode
operating at plate voltage 200V and grid voltage -6V. The plate
characteristics as shown in figure.

We know,

and

Also, we know

The plate resistance of a triode is 8k 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?

(a) mA

(b) V

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?

(a)

[As ]

And thus, grid voltage should be charged by,

(b)

V

or

V

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

Where v_{p} and v_{g}
are in volts and i_{p} in microamperes. The
tube is operated at v_{p}= 250v, v_{g}=-
20v. Calculate (a) the tube current, (b) the plate resistance, (c) the mutual
conductance and (d) the amplification factor.

(a)

mA

(b)

Differentiating above equation we get

Also,

(c)

(d)

The plate current in a triode can be written as

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

Differentiating we get,

Comparing (1) and (2) we get

or

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?

We know,

R_{L }= 60kΩ

## Chapter 19 - Electric Current through Gases Exercise 354

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.

Voltage gain,

Case 1:

Case 2:

Solving equation (1) and (2)

We get:

And

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.

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

Also, equivalent conductance is given as:

Now,

Equivalent amplification is given as:

Which is same as individual mutual conductance.

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