What is the voltage gain in a common emitter amplifier, where output resistance is `3 Omega` and load resistance is `24 Omega (beta=0.6)` ?

Options

A. 8.4
B. 4.8
C. 2.4
D. 480

Answer

To find the voltage gain in a common emitter amplifier, we can use the formula:

\[ A_V = \beta \cdot \frac{R_L}{R_{i}} \]

Where:
- \( A_V \) is the voltage gain,
- \( \beta \) is the current gain (given as 0.6),
- \( R_L \) is the load resistance (given as 24 Ω),
- \( R_i \) is the input resistance (given as 3 Ω).

### Step-by-Step Solution:

1. **Identify the values**:
- \( \beta = 0.6 \)
- \( R_L = 24 \, \Omega \)
- \( R_i = 3 \, \Omega \)

2. **Substitute the values into the voltage gain formula**:
\[ A_V = 0.6 \cdot \frac{24}{3} \]

3. **Calculate \( \frac{R_L}{R_i} \)**:
\[ \frac{R_L}{R_i} = \frac{24}{3} = 8 \]

4. **Now substitute back into the equation for \( A_V \)**:
\[ A_V = 0.6 \cdot 8 \]

5. **Perform the multiplication**:
\[ A_V = 4.8 \]

Thus, the voltage gain \( A_V \) in the common emitter amplifier is **4.8**.

### Final Answer:
The voltage gain \( A_V \) is **4.8**.

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