For a transistor `I_(e) = 25 mA and I_(b) = 1mA`. The value of current gain `alpha` will be :-

Options

A. `(25)/(24)`
B. `(24)/(25)`
C. `(25)/(26)`
D. `(26)/(25)`

Explanation

To find the value of current gain \( \alpha \) for the given transistor, we can follow these steps:

### Step 1: Understand the relationship between currents
The current gain \( \alpha \) is defined as the ratio of the collector current \( I_c \) to the emitter current \( I_e \):
\[ \alpha = \frac{I_c}{I_e} \]

### Step 2: Relate collector current to emitter and base currents
The collector current \( I_c \) can be expressed in terms of the emitter current \( I_e \) and the base current \( I_b \):
\[ I_c = I_e - I_b \]

### Step 3: Substitute the known values
Given:
- Emitter current \( I_e = 25 \, \text{mA} \)
- Base current \( I_b = 1 \, \text{mA} \)

We can substitute these values into the equation for \( I_c \):
\[ I_c = 25 \, \text{mA} - 1 \, \text{mA} = 24 \, \text{mA} \]

### Step 4: Calculate \( \alpha \)
Now we can substitute \( I_c \) and \( I_e \) into the equation for \( \alpha \):
\[ \alpha = \frac{I_c}{I_e} = \frac{24 \, \text{mA}}{25 \, \text{mA}} = \frac{24}{25} \]

### Step 5: Final answer
Thus, the value of the current gain \( \alpha \) is:
\[ \alpha = \frac{24}{25} \]