In a transistor circuit, when the base current is increased by `50mu A `keeping the collector voltage fixed at 2 V. the collector current increases by 1 mA The current gain of the transistor is

Options

A. 20
B. 40
C. 60
D. 80

Answer

To find the current gain (β) of the transistor, we can use the formula:

\[ \beta = \frac{\Delta I_C}{\Delta I_B} \]

where:
- \(\Delta I_C\) is the change in collector current,
- \(\Delta I_B\) is the change in base current.

### Step-by-Step Solution:

1. **Identify the change in base current (\(\Delta I_B\))**:
- Given that the base current is increased by \(50 \mu A\):
\[ \Delta I_B = 50 \mu A = 50 \times 10^{-6} A = 0.000050 A \]

2. **Identify the change in collector current (\(\Delta I_C\))**:
- Given that the collector current increases by \(1 mA\):
\[ \Delta I_C = 1 mA = 1 \times 10^{-3} A = 0.001 A \]

3. **Substitute the values into the formula for current gain (\(\beta\))**:
\[ \beta = \frac{\Delta I_C}{\Delta I_B} = \frac{0.001 A}{0.000050 A} \]

4. **Calculate \(\beta\)**:
\[ \beta = \frac{0.001}{0.000050} = \frac{1}{0.00005} = 20 \]

5. **Conclusion**:
- The current gain of the transistor is \(20\).

### Final Answer:
The current gain of the transistor is \(20\).