A common emitter transistor amplifier has a current gain of `50`. If the load resistance is `4k Omega`, and input resistance is `500 Omega`, the voltage gain of amplifier is.

Options

A. 160
B. 200
C. 400
D. none

Answer

To find the voltage gain of a common emitter transistor amplifier, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Current gain (β) = 50
- Load resistance (RL) = 4 kΩ = 4000 Ω
- Input resistance (RI) = 500 Ω

2. **Understand the Formula for Voltage Gain:**
- The voltage gain (Av) of a common emitter amplifier can be calculated using the formula:
\[ A_v = \frac{R_L}{R_I} \times \beta \]
where:
- \( R_L \) is the load resistance,
- \( R_I \) is the input resistance,
- \( \beta \) is the current gain.

3. **Substitute the Values into the Formula:**
- Substitute the known values into the voltage gain formula:
\[ A_v = \frac{4000 \, \Omega}{500 \, \Omega} \times 50 \]

4. **Calculate the Ratio of Resistances:**
- Calculate \( \frac{R_L}{R_I} \):
\[ \frac{4000}{500} = 8 \]

5. **Calculate the Voltage Gain:**
- Now multiply by the current gain (β):
\[ A_v = 8 \times 50 = 400 \]

6. **Final Result:**
- The voltage gain of the amplifier is:
\[ A_v = 400 \]

### Conclusion:
The voltage gain of the common emitter transistor amplifier is **400**.