A transistor is connected in a common emitter configuration.
The collector supply is 8 V and the voltage drop across a resistor of `800 Omega ` in
the collector circuit is 0.5 V. If the current gain factor `(alpha) ` is 0.96 , Find the base
current.

Explanation

To solve the problem step by step, we will follow the necessary calculations to find the base current (IB) of the transistor in a common emitter configuration.

### Step 1: Identify the given values
- Collector supply voltage (Vcc) = 8 V
- Voltage drop across collector resistor (V_R) = 0.5 V
- Collector resistor (R_C) = 800 Ω
- Current gain factor (α) = 0.96

### Step 2: Calculate the collector current (IC)
The collector current (IC) can be calculated using Ohm's Law:
\[ I_C = \frac{V_R}{R_C} \]
Substituting the given values:
\[ I_C = \frac{0.5 \, \text{V}}{800 \, \Omega} \]
Calculating IC:
\[ I_C = 6.25 \times 10^{-4} \, \text{A} \]
or
\[ I_C = 625 \, \mu A \]

### Step 3: Calculate the current gain factor (β)
The current gain factor (β) can be calculated from α using the formula:
\[ \beta = \frac{\alpha}{1 - \alpha} \]
Substituting the value of α:
\[ \beta = \frac{0.96}{1 - 0.96} \]
Calculating β:
\[ \beta = \frac{0.96}{0.04} = 24 \]

### Step 4: Calculate the base current (IB)
Using the relationship between collector current (IC) and base current (IB):
\[ \beta = \frac{I_C}{I_B} \]
We can rearrange this to find IB:
\[ I_B = \frac{I_C}{\beta} \]
Substituting the values of IC and β:
\[ I_B = \frac{6.25 \times 10^{-4} \, \text{A}}{24} \]
Calculating IB:
\[ I_B = 2.60416667 \times 10^{-5} \, \text{A} \]
or
\[ I_B \approx 26 \, \mu A \]

### Final Answer
The base current (IB) is approximately **26 µA**.