In CE transistor amplifier if the base current is increased by `20muA,` the collector current changes from 4 mA to 5 mA. The current gain of the transistor is

Options

A. 200
B. 50
C. 125
D. 250

Explanation

To find the current gain (β) of a common emitter transistor amplifier, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the change in base current (ΔIb)**:
- Given that the base current is increased by 20 µA.
- Convert this to amperes:
\[ \Delta I_b = 20 \, \mu A = 20 \times 10^{-6} \, A \]

2. **Identify the change in collector current (ΔIc)**:
- The collector current changes from 4 mA to 5 mA.
- Calculate the change:
\[ \Delta I_c = 5 \, mA - 4 \, mA = 1 \, mA \]
- Convert this to amperes:
\[ \Delta I_c = 1 \, mA = 1 \times 10^{-3} \, A \]

3. **Calculate the current gain (β)**:
- The current gain (β) is defined as the ratio of the change in collector current to the change in base current:
\[ \beta = \frac{\Delta I_c}{\Delta I_b} \]
- Substitute the values:
\[ \beta = \frac{1 \times 10^{-3}}{20 \times 10^{-6}} \]

4. **Perform the calculation**:
- Simplify the fraction:
\[ \beta = \frac{1}{20} \times 10^{3} = \frac{1000}{20} = 50 \]

5. **Conclusion**:
- The current gain (β) of the transistor is:
\[ \beta = 50 \]

### Final Answer:
The current gain of the transistor is **50**.

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