The current gain ofa transistor is 100. If the base current changes by 200 `mu`A, what is the change in collector current?

Options

A. 0.2mA
B. 20 mA
C. 2 mA
D. 200mA

Explanation

To solve the problem, we need to find the change in collector current (\( \Delta I_C \)) given the current gain (\( \beta \)) of the transistor and the change in base current (\( \Delta I_B \)).

### Step-by-Step Solution:

1. **Identify the given values:**
- Current gain of the transistor (\( \beta \)) = 100
- Change in base current (\( \Delta I_B \)) = 200 µA = \( 200 \times 10^{-6} \) A

2. **Use the formula for current gain:**
The current gain (\( \beta \)) is defined as the ratio of the change in collector current (\( \Delta I_C \)) to the change in base current (\( \Delta I_B \)):
\[ \beta = \frac{\Delta I_C}{\Delta I_B} \]

3. **Rearrange the formula to find \( \Delta I_C \):**
To find the change in collector current, we can rearrange the formula:
\[ \Delta I_C = \beta \times \Delta I_B \]

4. **Substitute the known values into the equation:**
\[ \Delta I_C = 100 \times (200 \times 10^{-6}) \]

5. **Calculate \( \Delta I_C \):**
\[ \Delta I_C = 100 \times 200 \times 10^{-6} = 20000 \times 10^{-6} = 0.02 \text{ A} = 20 \text{ mA} \]

6. **Convert to milliamperes (if necessary):**
Since the question may expect the answer in milliamperes:
\[ \Delta I_C = 20 \text{ mA} \]

### Final Answer:
The change in collector current (\( \Delta I_C \)) is **20 mA**.

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