In transistor, the change in base current from 400 microampere to 425 microampere,causes a change in collector current from 5 miliampere to 7.5 miliapmere keeping collector to emitter voltage constant at 10 V.Base to emitter voltage is 0.7V.then the current gain of transistor is ?

Explanation

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

### Step-by-Step Solution:

1. **Identify the changes in currents**:
- The change in base current (ΔIb) is calculated as:
\[ \Delta I_b = I_{b2} - I_{b1} = 425 \, \mu A - 400 \, \mu A = 25 \, \mu A \]
- Convert this to amperes:
\[ \Delta I_b = 25 \, \mu A = 25 \times 10^{-6} \, A \]

2. **Calculate the change in collector current (ΔIc)**:
- The change in collector current (ΔIc) is calculated as:
\[ \Delta I_c = I_{c2} - I_{c1} = 7.5 \, mA - 5 \, mA = 2.5 \, mA \]
- Convert this to amperes:
\[ \Delta I_c = 2.5 \, mA = 2.5 \times 10^{-3} \, A \]

3. **Calculate the current gain (β)**:
- The current gain (β) is defined as the ratio of the change in collector current to the change in base current:
\[ \beta = \frac{\Delta I_c}{\Delta I_b} \]
- Substitute the values:
\[ \beta = \frac{2.5 \times 10^{-3}}{25 \times 10^{-6}} \]

4. **Perform the calculation**:
- Simplifying the fraction:
\[ \beta = \frac{2.5}{25} \times \frac{10^{-3}}{10^{-6}} = \frac{2.5}{25} \times 10^{3} = 0.1 \times 10^{3} = 100 \]

5. **Final Result**:
- Therefore, the current gain (β) of the transistor is:
\[ \beta = 100 \]