Question

When the input voltage given to the combination of two common emitter amplifiers connected in series is \(20\ mV\), then the output voltage is \(30\ V\). If the voltage gain of one amplifier is \(25\), then the voltage gain of the other amplifier is

• A. \(60\)
• B. \(90\)
• C. \(80\)
• D. \(45\) \bigskip

Hint:

For cascaded amplifiers: \[ \text{Overall Gain}=(\text{Gain of first stage})(\text{Gain of second stage}) \] Always convert mV into volts before calculating voltage gain.

Answer 1

The Correct Option is A

Concept: When amplifiers are connected in series (cascade connection), the overall voltage gain is the product of the individual voltage gains. \[ A_v=A_{v1}\times A_{v2} \] Also, \[ A_v=\frac{V_o}{V_i} \] where \[ V_i=\text{Input voltage},\qquad V_o=\text{Output voltage} \]

Step 1: Calculate the overall voltage gain of the amplifier combination.
Given, \[ V_i=20\ mV=20\times10^{-3}V \] \[ V_o=30V \] Hence, \[ A_v=\frac{V_o}{V_i} \] \[ A_v=\frac{30}{20\times10^{-3}} \] \[ A_v=\frac{30}{0.02} \] \[ A_v=1500 \] Therefore, the combined voltage gain is \[ \boxed{1500} \]

Step 2: Use the cascade amplifier relation.
One amplifier has gain \[ A_{v1}=25 \] Let the gain of the second amplifier be \(A_{v2}\). Then, \[ 1500=25\times A_{v2} \] Therefore, \[ A_{v2}=\frac{1500}{25} \] \[ A_{v2}=60 \]

Step 3: Write the final answer.
The voltage gain of the other amplifier is \[ \boxed{60} \] Hence, the correct option is \[ \boxed{\text{(A)}} \]