For a transistor amplifier in common emitter configuration for load impedance of $1\;{\rm{k}}$ ( ${h_{fe}} = 50$ and ${h_{oe}} = 25 \times {10^{ - 6}}$) the current gain is

(A) $ - 48.78$.
(B) $ - 15.7$.
(C) $ - 24.8$.
(D) $ - 5.2$.

Hint: When a circuit or device has a power gain more than one then that circuit is known as an amplifier. The amplifiers are mostly used in the electronic components. In the common – emitter the current gain is obtained by the base and the collector circuit currents.


Complete step by step solution
Given: Transistor amplifier in $C - E$ configuration.
                            The load impedance ${R_L} = 1\;{\rm{k}}\Omega $.
                            ${h_{fe}} = 50$ and ${h_{oe}} = 25 \times {10^{ - 6}}$.

Express the formula of current gain.

${A_i} = - \dfrac{{{h_{fe}}}}{{1 + {h_{oe}}\;{R_L}}}$

Here,

${A_i}$ is the current gain.

Substitute $25 \times {10^{ - 6}}$ for ${h_{oe}}$, $50$ for ${h_{fe}}$ and $1\;{\rm{k}}\Omega $ for ${R_L}$ to obtain the current gain.

$\begin{array}{c}
{A_i} = - \dfrac{{50}}{{1 + 25 \times {{10}^{ - 6}} \times \;1 \times {{10}^3}\;\Omega }}\\
{A_i} = - \dfrac{{50}}{{1 + 25 \times {{10}^{ - 3}}}}\\
{A_i} = - 48.76
\end{array}$

Therefore, the correct option is (A).


Note: Make sure while solving this type of questions that the questions are asking about the common emitter or common base configuration. If we use common base configuration then the current gain will be different from current gain in common emitter configuration.