A common emitter amplifier has a voltage gain of `50`, an input impedence of `100 Omega` and an output impedence of `200 Omega`. The power gain of the of the amplifier is

Options

A. 500
B. 1000
C. 1250
D. 50

Explanation

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

### Step 1: Understand the Definitions
The power gain (P_gain) of an amplifier can be defined as the ratio of output power (P_out) to input power (P_in). It can also be expressed in terms of voltage gain (A_v) and the ratio of output current (I_out) to input current (I_in).

### Step 2: Write the Formula for Power Gain
The power gain can be expressed as:
\[ P_{\text{gain}} = \frac{P_{\text{out}}}{P_{\text{in}}} = \frac{V_{\text{out}} \cdot I_{\text{out}}}{V_{\text{in}} \cdot I_{\text{in}}} \]

### Step 3: Express Output Voltage and Input Voltage
Given that the voltage gain (A_v) is defined as:
\[ A_v = \frac{V_{\text{out}}}{V_{\text{in}}} = 50 \]

### Step 4: Relate Output Current and Input Current
The relationship between output current (I_out) and input current (I_in) can be derived from the input and output impedances:
- Input impedance (R_in) = 100 Ω
- Output impedance (R_out) = 200 Ω

Using the current relationship:
\[ \frac{I_{\text{out}}}{I_{\text{in}}} = \frac{R_{\text{in}}}{R_{\text{out}}} \]
We can express:
\[ I_{\text{out}} = \frac{R_{\text{in}}}{R_{\text{out}}} \cdot I_{\text{in}} = \frac{100}{200} \cdot I_{\text{in}} = 0.5 \cdot I_{\text{in}} \]

### Step 5: Substitute Values into Power Gain Formula
Now substituting the values into the power gain formula:
\[ P_{\text{gain}} = \frac{V_{\text{out}} \cdot I_{\text{out}}}{V_{\text{in}} \cdot I_{\text{in}}} \]
Substituting \( V_{\text{out}} = 50 \cdot V_{\text{in}} \) and \( I_{\text{out}} = 0.5 \cdot I_{\text{in}} \):
\[ P_{\text{gain}} = \frac{(50 \cdot V_{\text{in}}) \cdot (0.5 \cdot I_{\text{in}})}{V_{\text{in}} \cdot I_{\text{in}}} \]

### Step 6: Simplify the Expression
Cancelling \( V_{\text{in}} \) and \( I_{\text{in}} \) from the numerator and denominator:
\[ P_{\text{gain}} = 50 \cdot 0.5 = 25 \]

### Step 7: Calculate the Final Power Gain
Thus, the power gain of the amplifier is:
\[ P_{\text{gain}} = 25 \]

### Final Answer
The power gain of the common emitter amplifier is **25**.

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