In transistor, the change in base current from 100 microampere to 125 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 will follow these steps:

### Step 1: Calculate the change in base current (ΔIb)
The base current changes from 100 µA to 125 µA.

\[ \Delta I_b = I_{b2} - I_{b1} = 125 \, \mu A - 100 \, \mu A = 25 \, \mu A \]

### Step 2: Calculate the change in collector current (ΔIc)
The collector current changes from 5 mA to 7.5 mA.

\[ \Delta I_c = I_{c2} - I_{c1} = 7.5 \, mA - 5 \, mA = 2.5 \, mA \]

### Step 3: Use the formula for current gain (β)
The current gain (β) of the transistor is given by the ratio of the change in collector current to the change in base current.

\[ \beta = \frac{\Delta I_c}{\Delta I_b} \]

### Step 4: Substitute the values into the formula
Now, we will substitute the values we calculated for ΔIc and ΔIb into the formula.

\[ \beta = \frac{2.5 \, mA}{25 \, \mu A} \]

### Step 5: Convert units for consistency
To make calculations easier, we can convert mA to µA:

\[ 2.5 \, mA = 2.5 \times 10^3 \, \mu A = 2500 \, \mu A \]

Now substituting this value:

\[ \beta = \frac{2500 \, \mu A}{25 \, \mu A} \]

### Step 6: Calculate β
Now we can simplify the fraction:

\[ \beta = \frac{2500}{25} = 100 \]

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

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