Question

What is the voltage gain in a common emitter amplifier, where input resistance is $3.2$ and load resistance $24\,\Omega $ , $\beta = 0.6$ ?
(A) $8.4$
(B) $4.8$
(C) $2.4$
(D) $480$

Answer 1

Hint:Substitute the given data of the current gain, input resistance and the load resistance in the formula of the voltage gain given below to find out the voltage gain of the common emitter amplifier. Since the main work of the amplifier is to strengthen the input signal, the voltage gain represents the amplified voltage from the input voltage.

Formula used:
The formula of the voltage gain is given as
$v = \beta \left( {\dfrac{{{R_c}}}{{{R_b}}}} \right)$
Where $v$ is the voltage gain of the common emitter amplifier, $\beta $ is the current gain of it, ${R_c}$ is the load resistance and the ${R_b}$ is the input resistance.

Complete step by step solution:
It is given that the

Input resistance of the common emitter amplifier, ${R_b} = 3\,\,\Omega $

The load resistance, ${R_c} = 24\,\Omega $

The current gain, $\beta = 0.6$

The load resistance is always connected to the output of the amplifier and the input resistance is connected to the input of the amplifier. The input was given to the base emitter junction and the output of the amplifier is taken from the collector.

Using the formula of the voltage gain,

$v = \beta \left( {\dfrac{{{R_c}}}{{{R_b}}}} \right)$

Substituting the value of the current gain, load resistance and the input resistance in the above formula, we get

$v = 0.6\left( {\dfrac{{24}}{3}} \right)$

By performing the basic arithmetic operations in the above equation, we get

$v = \dfrac{{14.4}}{3}$

By further simplification of the above equation, we get

$v = 4.8\,$ .

Hence the value of the voltage gain for the common emitter amplifier is obtained as $4.8$ for the given values of the current gain and the resistances.

Thus the option (B) is correct.

Note:It is to be noted that the common emitter amplifier has the both of the current gain and also the voltage gain. Hence this problem contains both the parameters, but the common collector amplifier only has the voltage gain and does not have the current gain.