The input resistance of a transistor is `1000 Omega` on charging its base current by `10 muA`, the collector current increases by 2 mA. If a load resistance of `5 kOmega` is used in the circuit, the voltage gain of the amplifier is

Options

A. 100
B. 500
C. 1000
D. 1500

Explanation

To find the voltage gain of the amplifier given the input resistance, the change in base current, the change in collector current, and the load resistance, we can follow these steps:

### Step-by-Step Solution

1. **Identify Given Values**:
- Input resistance, \( R_{in} = 1000 \, \Omega \)
- Change in base current, \( \Delta I_B = 10 \, \mu A = 10 \times 10^{-6} \, A \)
- Change in collector current, \( \Delta I_C = 2 \, mA = 2 \times 10^{-3} \, A \)
- Load resistance, \( R_L = 5000 \, \Omega \)

2. **Calculate Current Gain (\( \beta \))**:
The current gain (\( \beta \)) is defined as the ratio of the change in collector current to the change in base current:
\[ \beta = \frac{\Delta I_C}{\Delta I_B} \]
Substituting the values:
\[ \beta = \frac{2 \times 10^{-3}}{10 \times 10^{-6}} = \frac{2 \times 10^{-3}}{10^{-5}} = 200 \]

3. **Calculate Voltage Gain (\( A_V \))**:
The voltage gain of the amplifier can be calculated using the formula:
\[ A_V = \beta \times \frac{R_L}{R_{in}} \]
Substituting the values:
\[ A_V = 200 \times \frac{5000}{1000} \]
Simplifying:
\[ A_V = 200 \times 5 = 1000 \]

4. **Conclusion**:
The voltage gain of the amplifier is \( 1000 \).

### Final Answer:
The voltage gain of the amplifier is \( 1000 \).

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