In a transistor, the collector current varies by 0.49 mA and emitter current varies by 0.50 mA. Then current gain `beta` is

Options

A. 49
B. 150
C. 99
D. 100

Answer

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

### Step 1: Understand the relationship between collector current (IC), emitter current (IE), and base current (IB).
The relationship is given by:
\[ I_E = I_C + I_B \]
Where:
- \( I_E \) is the emitter current,
- \( I_C \) is the collector current,
- \( I_B \) is the base current.

### Step 2: Given values.
From the question, we have:
- Variation in collector current, \( \Delta I_C = 0.49 \, \text{mA} \)
- Variation in emitter current, \( \Delta I_E = 0.50 \, \text{mA} \)

### Step 3: Calculate the base current (IB).
Using the relationship from Step 1, we can express the base current as:
\[ I_B = I_E - I_C \]
Substituting the given values:
\[ I_B = 0.50 \, \text{mA} - 0.49 \, \text{mA} \]
\[ I_B = 0.01 \, \text{mA} \]

### Step 4: Calculate the current gain (β).
The current gain (β) is defined as:
\[ \beta = \frac{I_C}{I_B} \]
Substituting the values we calculated:
\[ \beta = \frac{0.49 \, \text{mA}}{0.01 \, \text{mA}} \]
\[ \beta = 49 \]

### Conclusion:
The current gain \( \beta \) is 49.

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