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. 75
B. 100
C. 150
D. 50

Answer

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

### Step-by-Step Solution:

1. **Identify the given values:**
- Initial base current (I_B1) = 100 µA = 0.1 mA
- Final base current (I_B2) = 200 µA = 0.2 mA
- Initial collector current (I_C1) = 5 mA
- Final collector current (I_C2) = 10 mA

2. **Calculate the change in base current (ΔI_B):**
\[ ΔI_B = I_B2 - I_B1 = 200 \mu A - 100 \mu A = 100 \mu A = 0.1 mA \]

3. **Calculate the change in collector current (ΔI_C):**
\[ ΔI_C = I_C2 - I_C1 = 10 mA - 5 mA = 5 mA \]

4. **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:
\[ β = \frac{ΔI_C}{ΔI_B} \]
Substituting the values:
\[ β = \frac{5 mA}{0.1 mA} = 50 \]

5. **Final Answer:**
The current gain (β) of the transistor is **50**.