Calculate the current amplification factor `beta `when change in collector current is 1mA and change in base current is `20 mu A`.

Options

A. 50
B. 25
C. 75
D. 100

Answer

To calculate the current amplification factor \( \beta \), we can follow these steps:

### Step 1: Understand the formula for \( \beta \)
The current amplification factor \( \beta \) is defined as the ratio of the change in collector current (\( \Delta I_C \)) to the change in base current (\( \Delta I_B \)):
\[ \beta = \frac{\Delta I_C}{\Delta I_B} \]

### Step 2: Identify the given values
From the problem, we have:
- Change in collector current, \( \Delta I_C = 1 \, \text{mA} = 1 \times 10^{-3} \, \text{A} \)
- Change in base current, \( \Delta I_B = 20 \, \mu\text{A} = 20 \times 10^{-6} \, \text{A} \)

### Step 3: Substitute the values into the formula
Now, we can substitute the values into the formula for \( \beta \):
\[ \beta = \frac{1 \times 10^{-3}}{20 \times 10^{-6}} \]

### Step 4: Simplify the expression
To simplify this expression, we can rewrite it as:
\[ \beta = \frac{1}{20} \times \frac{10^{-3}}{10^{-6}} = \frac{1}{20} \times 10^{3} \]
This simplifies to:
\[ \beta = \frac{10^{3}}{20} \]

### Step 5: Perform the division
Now, we can calculate:
\[ \beta = \frac{1000}{20} = 50 \]

### Conclusion
Thus, the current amplification factor \( \beta \) is:
\[ \beta = 50 \]

### Final Answer
The correct answer is \( \beta = 50 \).

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