Power gain for `N-P-N` transistor is `10^(@)`, input resistance `100Omega` and output resistance `10000Omega`. Find out current gain.

Options

A. 100
B. 150
C. 200
D. 50

Answer

To find the current gain (β) of an N-P-N transistor given the power gain, input resistance, and output resistance, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values**:
- Power Gain (P) = \(10^0 = 1\)
- Input Resistance (R_in) = \(100 \, \Omega\)
- Output Resistance (R_out) = \(10000 \, \Omega\)

2. **Understand the Relationship**:
- The power gain (P) can be expressed in terms of current gain (β) and resistances:
\[ P = \frac{P_{out}}{P_{in}} = \frac{I_{out}^2 \cdot R_{out}}{I_{in}^2 \cdot R_{in}} \]
- This can be rearranged to:
\[ P = \left(\frac{I_{out}}{I_{in}}\right)^2 \cdot \frac{R_{out}}{R_{in}} = \beta^2 \cdot \frac{R_{out}}{R_{in}} \]

3. **Substitute the Known Values**:
- Substitute the known values into the equation:
\[ 1 = \beta^2 \cdot \frac{10000}{100} \]
- Simplifying the fraction:
\[ 1 = \beta^2 \cdot 100 \]

4. **Solve for β²**:
- Rearranging gives:
\[ \beta^2 = \frac{1}{100} \]

5. **Calculate β**:
- Taking the square root of both sides:
\[ \beta = \sqrt{100} = 10 \]

6. **Final Answer**:
- The current gain (β) is \(10\).