An N-P-N transistor is connected in common-emitter configuration in which collector supply is 8V and the voltage drop across the load resistance of `800Omega` connected in the collector circuit is 0.8V. If current amplification factor is 25/26 (If the internal resistance of the transistor is `200Omega`), the collector-emitter voltage, voltage gain and power gain are respectively.

Options

A. `5.2V,1.86,3`
B. `6.2V, 186, 5.5`
C. `7.2V, 3.86, 3.698`
D. `4.91, 3.15`

Explanation

To solve the problem step by step, we will find the collector-emitter voltage (V_CE), voltage gain (A_V), and power gain (P_G) for the given N-P-N transistor in a common-emitter configuration.

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

The voltage drop across the load resistance (R_L) is given as 0.8V, and the load resistance is 800Ω.

Using Ohm's law:
\[ I_C = \frac{V_{drop}}{R_L} = \frac{0.8V}{800Ω} = 1 \times 10^{-3} A = 1 mA \]

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

The collector supply voltage (V_CC) is given as 8V. The voltage drop across the internal resistance (R_C) of the transistor is calculated using the collector current (I_C) and the internal resistance (R_C = 200Ω):

\[ V_{RC} = I_C \times R_C = 1 \times 10^{-3} A \times 200Ω = 0.2V \]

Now, we can calculate V_CE:
\[ V_{CE} = V_{CC} - V_{RC} = 8V - 0.2V = 7.8V \]

### Step 3: Calculate the Voltage Gain (A_V)

The voltage gain (A_V) can be calculated using the formula:
\[ A_V = \beta \times \frac{R_L}{R_C} \]
Where:
- \(\beta = \frac{25}{26}\)
- \(R_L = 800Ω\)
- \(R_C = 200Ω\)

Substituting the values:
\[ A_V = \frac{25}{26} \times \frac{800}{200} = \frac{25}{26} \times 4 = \frac{100}{26} \approx 3.846 \]

### Step 4: Calculate the Power Gain (P_G)

The power gain (P_G) can be calculated using the formula:
\[ P_G = \beta^2 \times \frac{R_L}{R_C} \]

Calculating \(\beta^2\):
\[ \beta^2 = \left(\frac{25}{26}\right)^2 = \frac{625}{676} \]

Now substituting into the power gain formula:
\[ P_G = \frac{625}{676} \times \frac{800}{200} = \frac{625}{676} \times 4 = \frac{2500}{676} \approx 3.698 \]

### Final Results

- Collector-Emitter Voltage (V_CE) = 7.8V
- Voltage Gain (A_V) ≈ 3.846
- Power Gain (P_G) ≈ 3.698