In a common emitter (CE) amplifier having a voltage gain G, the transistor used has transconductor 0.03 mho and current gain 25. If the above transistor is replaced with another one with transconductance 0.02 mho and current gain 20, the voltage gain will

Options

A. `(2)/(3)G`
B. `1.5G`
C. `(1)/(3)G`
D. `(5)/(4)G`

Answer

To solve the problem, we need to determine the voltage gain of the second transistor in a common emitter amplifier configuration. We will use the relationship between transconductance (g) and voltage gain (G) for the two transistors.

### Step-by-Step Solution:

1. **Understand the Voltage Gain Formula**:
The voltage gain (G) of a common emitter amplifier can be expressed as:
\[ G = g_m \cdot R_C \]
where \( g_m \) is the transconductance and \( R_C \) is the collector resistance.

2. **Identify Given Values for the First Transistor**:
For the first transistor:
- Transconductance, \( g_{m1} = 0.03 \, \text{mho} \)
- Current gain, \( \beta_1 = 25 \)
- Voltage gain, \( G_1 = G \)

3. **Identify Given Values for the Second Transistor**:
For the second transistor:
- Transconductance, \( g_{m2} = 0.02 \, \text{mho} \)
- Current gain, \( \beta_2 = 20 \)

4. **Relate the Voltage Gains of the Two Transistors**:
Since the collector resistance \( R_C \) remains the same for both transistors, we can write:
\[ \frac{G_1}{G_2} = \frac{g_{m1}}{g_{m2}} \]
Substituting the known values:
\[ \frac{G}{G_2} = \frac{0.03}{0.02} \]

5. **Calculate the Ratio**:
\[ \frac{G}{G_2} = \frac{3}{2} \]
This implies:
\[ G_2 = \frac{2}{3} G \]

6. **Conclusion**:
The voltage gain of the second transistor \( G_2 \) is:
\[ G_2 = \frac{2}{3} G \]

### Final Answer:
The voltage gain of the second transistor is \( \frac{2}{3} G \).