Question

The current gain in the common emitter amplifier mode of a transistor is 10. The input impedance is $20k\Omega $ and load resistance is $100k\Omega $. The power gain is:
A. 300
B. 500
C. 200
D. 100

Answer 1

Hint: we have the current gain of the circuit. Find the resistance gain of the circuit by using the given input and output resistance in the question. Then use the equation for power gain and put these values to get the answer.
Formula used:
The power gain of an amplifier is given by the expression,
$\text{power gain = }{{\left( \text{current gain} \right)}^{2}}\text{ }\times \text{ resistance gain}$

Complete step by step answer:
The current gain of an amplifier in a common emitter mode is given by the ratio of the collector current to the base current. It can also be defined as the ratio of the output current to the input current.
The current gain is given as, $\beta =10$
The input impedance on the circuit is given as, ${{R}_{i}}=20k\Omega $
The output resistance or the load resistance of the amplifier is given by, ${{R}_{o}}=100k\Omega $.
Now the resistance gain of an amplifier is defined as the ratio of the output resistance to the input resistance.
So, resistance gain will be, $\dfrac{{{R}_{o}}}{{{R}_{i}}}=\dfrac{100}{20}=5$
Now, the power gain of an amplifier is defined as the ratio of the output power to the input power. It can be mathematically expressed as the product of the square of the current gain and the resistance gain. So, we can write that,
$\begin{align}
  & \text{power gain = }{{\left( \text{current gain} \right)}^{2}}\text{ }\times \text{ resistance gain} \\
 & \text{power gain =1}{{\text{0}}^{2}}\times 5 \\
 & \text{power gain =50} \\
\end{align}$
So, the current gain of the amplifier is 500.
The correct option is (B)
Note: the common emitter amplifier is also known as the voltage amplifier. The input is given in the base and the output is measured at the collector terminal. Here the emitter is common for both the terminals.