In transistor, the change in base current from 450 microampere to 500 microampere,causes a change in collector current from 5.5 miliampere to 10.5 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 will follow these steps:

### Step 1: Identify the given values
- Initial base current (Ib1) = 450 µA = 450 × 10^(-6) A
- Final base current (Ib2) = 500 µA = 500 × 10^(-6) A
- Initial collector current (Ic1) = 5.5 mA = 5.5 × 10^(-3) A
- Final collector current (Ic2) = 10.5 mA = 10.5 × 10^(-3) A

### Step 2: Calculate the change in base current (ΔIb)
\[ \Delta I_b = I_{b2} - I_{b1} = (500 \times 10^{-6}) - (450 \times 10^{-6}) = 50 \times 10^{-6} \text{ A} \]

### Step 3: Calculate the change in collector current (ΔIc)
\[ \Delta I_c = I_{c2} - I_{c1} = (10.5 \times 10^{-3}) - (5.5 \times 10^{-3}) = 5 \times 10^{-3} \text{ A} \]

### Step 4: 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:
\[ \beta = \frac{\Delta I_c}{\Delta I_b} = \frac{5 \times 10^{-3}}{50 \times 10^{-6}} \]

### Step 5: Simplify the calculation
\[ \beta = \frac{5 \times 10^{-3}}{50 \times 10^{-6}} = \frac{5}{50} \times 10^{3} = \frac{1}{10} \times 10^{3} = 100 \]

### Conclusion
The current gain (β) of the transistor is **100**.

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