The current gain in the common emitter mode of a transistor is 10. The input impedance is `20kOmega` and load of resistance is `100k Omega`. The power gain is

Options

A. 300
B. 500
C. 200
D. 100

Answer

To find the power gain of a common emitter transistor given the current gain, input impedance, and load resistance, we can follow these steps:

### Step 1: Understand the Given Data
We have the following information:
- Current gain (β) = 10
- Input impedance (R_in) = 20 kΩ
- Load resistance (R_out) = 100 kΩ

### Step 2: Formula for Power Gain
The power gain (P_gain) in a common emitter configuration can be expressed as:
\[ P_{\text{gain}} = \beta \times V_{\text{gain}} \]
Where \( V_{\text{gain}} \) can be expressed in terms of current gain and resistance gain:
\[ V_{\text{gain}} = \beta \times \frac{R_{\text{out}}}{R_{\text{in}}} \]

### Step 3: Substitute the Values
Now, we can substitute the values into the formula:
1. Calculate the resistance gain:
\[ \frac{R_{\text{out}}}{R_{\text{in}}} = \frac{100 \text{ kΩ}}{20 \text{ kΩ}} = 5 \]

2. Now substitute into the power gain formula:
\[ P_{\text{gain}} = \beta^2 \times \frac{R_{\text{out}}}{R_{\text{in}}} \]
\[ P_{\text{gain}} = 10^2 \times 5 \]
\[ P_{\text{gain}} = 100 \times 5 = 500 \]

### Step 4: Conclusion
The power gain of the transistor in common emitter mode is **500**.