A CE amplifier has voltage gain of 50, an input impedance of 2000 ohm and an output impedance of 400 ohm. The power gain of the amplifier will be

Options

A. 22500
B. 12500
C. 32500
D. 4100

Answer

To find the power gain of the common emitter (CE) amplifier, we can follow these steps:

### Step 1: Identify the given values
- Voltage gain (Av) = 50
- Input impedance (Zi) = 2000 ohms
- Output impedance (Zo) = 400 ohms

### Step 2: Calculate the resistance gain (Rg)
Resistance gain is defined as the ratio of output impedance to input impedance. The formula for resistance gain is:
\[ Rg = \frac{Zo}{Zi} \]

Substituting the given values:
\[ Rg = \frac{400 \, \text{ohm}}{2000 \, \text{ohm}} = \frac{1}{5} \]

### Step 3: Calculate the power gain (Pg)
Power gain can be calculated using the formula:
\[ Pg = \frac{(Av)^2}{Rg} \]

Substituting the values we have:
\[ Pg = \frac{(50)^2}{\frac{1}{5}} \]

Calculating \( (50)^2 \):
\[ (50)^2 = 2500 \]

Now substituting this value into the power gain formula:
\[ Pg = \frac{2500}{\frac{1}{5}} = 2500 \times 5 = 12500 \]

### Final Answer
The power gain of the amplifier is:
\[ Pg = 12500 \]

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