A transistor connected at common emitter mode contains load resistance of `5 k Omega`. If the input peak voltage is 5 mV and the current gain is 50, find the voltage gain.

Options

A. 250
B. 500
C. 125
D. 50

Answer

To solve the problem step by step, we will use the formula for voltage gain in a common emitter transistor configuration.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Load Resistance (\( R_L \)) = \( 5 \, k\Omega = 5000 \, \Omega \)
- Input Peak Voltage (\( V_{in} \)) = \( 5 \, mV = 0.005 \, V \)
- Current Gain (\( \beta \)) = \( 50 \)

2. **Understand the Formula for Voltage Gain:**
The voltage gain (\( A_v \)) in a common emitter configuration can be calculated using the formula:
\[ A_v = \beta \times \frac{R_L}{R_{in}} \]
where \( R_{in} \) is the input resistance. For this problem, we will assume a typical value for \( R_{in} \) which is \( 1000 \, \Omega \) (1 kΩ).

3. **Substitute the Values into the Formula:**
Now, we can substitute the known values into the voltage gain formula:
\[ A_v = 50 \times \frac{5000 \, \Omega}{1000 \, \Omega} \]

4. **Calculate the Voltage Gain:**
First, calculate the fraction:
\[ \frac{5000}{1000} = 5 \]
Now substitute this back into the equation:
\[ A_v = 50 \times 5 = 250 \]

5. **Final Result:**
Therefore, the voltage gain \( A_v \) is:
\[ A_v = 250 \]

### Conclusion:
The voltage gain of the transistor in common emitter mode is **250**.