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Question: In a common emitter transistor amplifier the audio signal voltage across the collector is \(3\,V\). ...

In a common emitter transistor amplifier the audio signal voltage across the collector is 3V3\,V. The resistance of the collector is 3KΩ3\,K\Omega . If current gain is 100100 and the base resistance is 2KΩ2\,K\Omega , the voltage and power gain of the amplifier is:
(A) 2020 and 20002000
(B) 200200 and 10001000
(C) 1515 and 200200
(D) 150150 and 1500015000

Explanation

Solution

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=β(RcRb)V = \beta \left( {\dfrac{{{R_c}}}{{{R_b}}}} \right)
Where VV is the voltage gain in the circuit, β\beta is the current gain of the amplifier circuit, Rc{R_c} is the resistance of the collector and Rb{R_b} is the base resistance.
(2) Power of the amplifier is given by
P=VβP = V\beta
Where PP is the power of the amplifier.

Complete step by step solution:
It is given that the
Voltage of the given amplifier, v=3Vv = 3\,V
Resistance of the collector, Rc=3Ω{R_c} = 3\,\Omega
Base resistance of the amplifier, Rb=2Ω{R_b} = 2\,\Omega
Current gain of the circuit, β=100A\beta = 100\,A
The voltage gain of calculated from the formula (1)
V=β(RcRb)V = \beta \left( {\dfrac{{{R_c}}}{{{R_b}}}} \right)
Substitute the values of the known parameters in the above step.
V=100(32)V = 100\left( {\dfrac{3}{2}} \right)
V=150VV = 150\,V
Hence the voltage gain of the given amplifier is obtained as 150V150\,V .
The formula (2) of the power gain is used.
P=VβP = V\beta
Substituting the values of the parameters in the above formula.
P=150×100P = 150 \times 100
P=15000WP = 15000\,W
Hence the power of the amplifier is calculated as 1500015000.

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.