Question

A transistor is used in common emitter mode in an amplifier circuit. When a signal of $20\text{mV}$ is added to the base-emitter voltage, the base current changes by $20\mu \text{A}$ and current gain is $100$. The transconductance is,

• A. $0.1\text{mho}$
• B. $0.2\text{mho}$
• C. $0.3\text{mho}$
• D. $0.4\text{mho}$

Answer 1

The correct option is A $0.1\text{mho}$

Given:
Base-emitter voltage, $\Delta V_{BE}=20\text{mV}=2\times {10}^{-2}\text{V}$

Change in base current, $\Delta I_B=20\mu \text{A}$

Current gain, $\beta =100$

So, $\beta =\frac{\Delta I_C}{\Delta I_B}$

$\Rightarrow \Delta I_C=\beta \Delta I_B=100\times 20\times {10}^{-6}=2\times {10}^{-3}\text{A}$

Now, transconductance,
$g_m=\frac{\Delta I_C}{\Delta V_{BE}}=\frac{2\times {10}^{-3}}{2\times {10}^{-2}}=0.1\text{mho}$

Hence, $\left(A\right)$ is the correct answer.

$$\begin{array}{c}\text{Why this question?}\\ \text{Concept:-Trans conductance is the property of}\\ \text{certain electronic components.}\\ \text{It is reciprocal of resistance.}\end{array}$$