What is the voltage gain in a common emitter amplifier, where input resistance is `3Omega` and load resistance `24Omega` and `beta=61` ?

Options

A. 8.4
B. 488
C. 240
D. 0

Explanation

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

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

Where:
- \( A_V \) is the voltage gain,
- \( \beta \) is the current gain (given as 61),
- \( R_L \) is the load resistance (given as 24 ohms),
- \( R_{in} \) is the input resistance (given as 3 ohms).

### Step-by-Step Solution:

1. **Identify the given values:**
- Input resistance, \( R_{in} = 3 \, \Omega \)
- Load resistance, \( R_L = 24 \, \Omega \)
- Beta, \( \beta = 61 \)

2. **Substitute the values into the voltage gain formula:**
\[ A_V = \beta \cdot \frac{R_L}{R_{in}} = 61 \cdot \frac{24}{3} \]

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

4. **Now substitute back to find \( A_V \):**
\[ A_V = 61 \cdot 8 \]

5. **Perform the multiplication:**
\[ A_V = 488 \]

### Final Answer:
The voltage gain \( A_V \) in the common emitter amplifier is **488**.