In a common emitter amplifier , the load resistance of the output circuit is 500 times the resistance of the input circuit. If ` alpha = 0.98 ` , then find the voltage gain and power gain .

Explanation

To solve the problem step by step, we will follow the given information and apply the relevant formulas for a common emitter amplifier.

### Step 1: Understand the Given Information
- Load resistance \( R_L \) is 500 times the input resistance \( R_{in} \).
- \( \alpha = 0.98 \).

### Step 2: Find the Current Gain \( \beta \)
In a common emitter amplifier, the relationship between \( \alpha \) (current gain for common base) and \( \beta \) (current gain for common emitter) is given by the formula:
\[ \beta = \frac{\alpha}{1 - \alpha} \]
Substituting the given value of \( \alpha \):
\[ \beta = \frac{0.98}{1 - 0.98} = \frac{0.98}{0.02} = 49 \]

### Step 3: Determine the Voltage Gain \( A_V \)
The voltage gain \( A_V \) in a common emitter amplifier can be calculated using the formula:
\[ A_V = \beta \cdot \frac{R_L}{R_{in}} \]
Given that \( R_L = 500 \cdot R_{in} \), we can substitute this into the equation:
\[ A_V = \beta \cdot 500 \]
Substituting the value of \( \beta \):
\[ A_V = 49 \cdot 500 = 24500 \]

### Step 4: Calculate the Power Gain \( A_P \)
The power gain \( A_P \) can be calculated by multiplying the voltage gain \( A_V \) by the current gain \( \beta \):
\[ A_P = A_V \cdot \beta \]
Substituting the values we have:
\[ A_P = 24500 \cdot 49 \]
Calculating this:
\[ A_P = 1200500 \]

### Final Results
- Voltage Gain \( A_V = 24500 \)
- Power Gain \( A_P = 1200500 \)