An `N-P-N` transistor is being used in CE mode for which the current transfer ratio is `alpha=(25)/(26)`. The input resistance is `1000Omega` and amplitude of A.C. input voltage is 10 mV. The amplitude of the amplified output collector current is

Options

A. `25muA`
B. `250muA`
C. `125muA`
D. `50muA`

Answer

To solve the problem, we need to find the amplitude of the amplified output collector current for an N-P-N transistor in common emitter mode, given the current transfer ratio (alpha), input resistance, and the amplitude of the A.C. input voltage.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Current transfer ratio, \( \alpha = \frac{25}{26} \)
- Input resistance, \( R_I = 1000 \, \Omega \)
- Amplitude of A.C. input voltage, \( V_I = 10 \, \text{mV} = 10 \times 10^{-3} \, \text{V} \)

2. **Calculate Beta:**
- The relationship between alpha and beta is given by:
\[ \beta = \frac{\alpha}{1 - \alpha} \]
- Substituting the value of alpha:
\[ \beta = \frac{\frac{25}{26}}{1 - \frac{25}{26}} = \frac{\frac{25}{26}}{\frac{1}{26}} = 25 \]

3. **Calculate Base Current (\( I_B \)):**
- The base current can be calculated using Ohm's law:
\[ I_B = \frac{V_I}{R_I} \]
- Substituting the known values:
\[ I_B = \frac{10 \times 10^{-3}}{1000} = 10 \times 10^{-6} \, \text{A} = 10 \, \mu\text{A} \]

4. **Calculate Collector Current (\( I_C \)):**
- The collector current is related to the base current by the formula:
\[ I_C = \beta \times I_B \]
- Substituting the values of beta and base current:
\[ I_C = 25 \times 10 \, \mu\text{A} = 250 \, \mu\text{A} \]

5. **Final Answer:**
- The amplitude of the amplified output collector current is \( 250 \, \mu\text{A} \).

### Summary:
The amplitude of the amplified output collector current is \( 250 \, \mu\text{A} \).