An n - p- n transistor is connected in common - emitter configuraration in which collector supply is 8 V and the voltage drop across the load resistance of ` 800 Omega ` connected in the collector circuit is 0.8 V . If current amplification factor is 25 , determine collector - emitter voltage and base current . If the internal resistance of the transistor is ` 200 Omega ` , calculate the voltage gain and the power gain.

Explanation

To solve the problem step by step, we will determine the collector-emitter voltage (V_CE), the base current (I_B), the voltage gain (A_V), and the power gain (A_P) of the n-p-n transistor in common-emitter configuration.

### Step 1: Calculate the Collector Current (I_C)

The collector current (I_C) can be calculated using the formula:

\[ I_C = \frac{V_{RL}}{R_L} \]

Where:
- \( V_{RL} \) is the voltage drop across the load resistance (0.8 V)
- \( R_L \) is the load resistance (800 Ω)

Substituting the values:

\[ I_C = \frac{0.8 \, \text{V}}{800 \, \Omega} = 10^{-3} \, \text{A} = 1 \, \text{mA} \]

### Step 2: Calculate the Collector-Emitter Voltage (V_CE)

The collector-emitter voltage (V_CE) can be calculated using the formula:

\[ V_{CE} = V_{CC} - I_C \times R_L \]

Where:
- \( V_{CC} \) is the collector supply voltage (8 V)

Substituting the values:

\[ V_{CE} = 8 \, \text{V} - (10^{-3} \, \text{A} \times 800 \, \Omega) = 8 \, \text{V} - 0.8 \, \text{V} = 7.2 \, \text{V} \]

### Step 3: Calculate the Base Current (I_B)

The base current (I_B) can be calculated using the current amplification factor (β):

\[ I_B = \frac{I_C}{\beta} \]

Where:
- \( \beta \) is the current amplification factor (25)

Substituting the values:

\[ I_B = \frac{10^{-3} \, \text{A}}{25} = 40 \times 10^{-6} \, \text{A} = 40 \, \mu\text{A} \]

### Step 4: Calculate the Voltage Gain (A_V)

The voltage gain (A_V) can be calculated using the formula:

\[ A_V = \frac{\beta \times R_L}{R_{internal}} \]

Where:
- \( R_{internal} \) is the internal resistance of the transistor (200 Ω)

Substituting the values:

\[ A_V = \frac{25 \times 800}{200} = 100 \]

### Step 5: Calculate the Power Gain (A_P)

The power gain (A_P) can be calculated using the formula:

\[ A_P = \frac{\beta^2 \times R_L}{R_{internal}} \]

Substituting the values:

\[ A_P = \frac{25^2 \times 800}{200} = \frac{625 \times 800}{200} = 2500 \]

### Summary of Results

- Collector-Emitter Voltage (V_CE): 7.2 V
- Base Current (I_B): 40 µA
- Voltage Gain (A_V): 100
- Power Gain (A_P): 2500