Question

In a common emitter transistor amplifier the audio signal voltage across the collector is $3\,V$. The resistance of the collector is $3\,K\Omega $. If current gain is $100$ and the base resistance is $2\,K\Omega $, the voltage and power gain of the amplifier is:
(A) $20$ and $2000$
(B) $200$ and $1000$
(C) $15$ and $200$
(D) $150$ and $15000$

Answer 1

Hint:To find the voltage gain, use the formula and substitute the values of the current gain, resistance of the collector and the base resistances. Substitute the calculated value of the voltage gain and the current gain, to find the value of the power gain of the amplifier.

Useful formula:
(1) The voltage gain is given as
$V = \beta \left( {\dfrac{{{R_c}}}{{{R_b}}}} \right)$
Where $V$ is the voltage gain in the circuit, $\beta $ is the current gain of the amplifier circuit, ${R_c}$ is the resistance of the collector and ${R_b}$ is the base resistance.
(2) Power of the amplifier is given by
$P = V\beta $
Where $P$ is the power of the amplifier.

Complete step by step solution:
It is given that the
Voltage of the given amplifier, $v = 3\,V$
Resistance of the collector, ${R_c} = 3\,\Omega $
Base resistance of the amplifier, ${R_b} = 2\,\Omega $
Current gain of the circuit, $\beta = 100\,A$
The voltage gain of calculated from the formula (1)
$V = \beta \left( {\dfrac{{{R_c}}}{{{R_b}}}} \right)$
Substitute the values of the known parameters in the above step.
$V = 100\left( {\dfrac{3}{2}} \right)$
$V = 150\,V$
Hence the voltage gain of the given amplifier is obtained as $150\,V$ .
The formula (2) of the power gain is used.
$P = V\beta $
Substituting the values of the parameters in the above formula.
$P = 150 \times 100$
$P = 15000\,W$
Hence the power of the amplifier is calculated as $15000$.

Thus the option (D) is correct.

Note:The term gain in the current, voltage and the power is mainly used in the amplifier. These gains are calculated based on the output and the input ratio of the above specified terms. This mainly resembles the gain in the output when compared to the input.