A transistor is operated in common emitter configuration at `V_(c)=2 V` such that a change in the base current from `100 muA` to `200 muA` produces a change in the collector current from `5 mA` to `10 mA`. The current gain is

Options

A. 50
B. 75
C. 100
D. 150

Explanation

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

### Step-by-Step Solution:

1. **Identify the Change in Base Current (ΔIB)**:
- The base current changes from \(100 \mu A\) to \(200 \mu A\).
- Therefore,
\[ \Delta I_B = I_{B2} - I_{B1} = 200 \mu A - 100 \mu A = 100 \mu A \]

2. **Identify the Change in Collector Current (ΔIC)**:
- The collector current changes from \(5 mA\) to \(10 mA\).
- Therefore,
\[ \Delta I_C = I_{C2} - I_{C1} = 10 mA - 5 mA = 5 mA \]

3. **Calculate the Current Gain (β)**:
- The current gain (β) is given by the formula:
\[ \beta = \frac{\Delta I_C}{\Delta I_B} \]
- Substituting the values we found:
\[ \beta = \frac{5 mA}{100 \mu A} \]

4. **Convert Units for Calculation**:
- Convert \(5 mA\) to microamperes:
\[ 5 mA = 5 \times 10^3 \mu A = 5000 \mu A \]
- Now substituting back into the equation:
\[ \beta = \frac{5000 \mu A}{100 \mu A} \]

5. **Simplify the Calculation**:
- Simplifying the fraction:
\[ \beta = \frac{5000}{100} = 50 \]

### Final Answer:
The current gain (β) of the transistor is \(50\).

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