In a common emitter transistor transistor amplifier, the audio signal voltage across the collector is 3 volt. The resistance of collector is `3kOmega`. If current gain is 100 and the base resistance is `2kOmega`, the voltage and power gain of the amplifier are

Options

A. 200 and 100
B. 15 and 200
C. 150 and 15000
D. 20 and 2000

Answer

To solve the problem step by step, we need to find the voltage gain and power gain of the common emitter transistor amplifier using the given parameters.

### Step 1: Identify the given values
- Collector voltage (V_C) = 3 V
- Collector resistance (R_C) = 3 kΩ = 3000 Ω
- Current gain (β) = 100
- Base resistance (R_B) = 2 kΩ = 2000 Ω

### Step 2: Calculate the voltage gain (A_V)
The voltage gain of a common emitter amplifier can be calculated using the formula:
\[ A_V = \beta \times \frac{R_C}{R_B} \]

Substituting the given values:
\[ A_V = 100 \times \frac{3000}{2000} \]

### Step 3: Simplify the fraction
Calculating the fraction:
\[ \frac{3000}{2000} = 1.5 \]

### Step 4: Calculate the voltage gain
Now substituting back into the voltage gain formula:
\[ A_V = 100 \times 1.5 = 150 \]

### Step 5: Calculate the power gain (A_P)
The power gain can be calculated using the formula:
\[ A_P = \beta \times A_V \]

Substituting the values we have:
\[ A_P = 100 \times 150 \]

### Step 6: Calculate the power gain
Calculating the power gain:
\[ A_P = 15000 \]

### Final Results
- Voltage Gain (A_V) = 150
- Power Gain (A_P) = 15000

### Summary
The voltage gain of the amplifier is 150, and the power gain is 15000.