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

Options

A. `200 and 1000`
B. `15 and 200`
C. `150 and 15000`
D. `20 and 2000`

Answer

To solve the problem step by step, we will calculate the voltage gain and power gain of the common emitter transistor amplifier using the given data.

### Step 1: Identify the Given Data
- Collector voltage (Vc) = 3 V
- Collector resistance (Rc) = 3 kΩ = 3000 Ω
- Current gain (β) = 100
- Base resistance (Rb) = 2 kΩ = 2000 Ω

### Step 2: Calculate the Collector Current (Ic)
Using Ohm's Law, we can find the collector current (Ic):
\[ Ic = \frac{Vc}{Rc} = \frac{3 \text{ V}}{3000 \text{ Ω}} = 10^{-3} \text{ A} = 1 \text{ mA} \]

### Step 3: Calculate the Base Current (Ib)
Using the current gain (β), we can find the base current (Ib):
\[ Ib = \frac{Ic}{β} = \frac{10^{-3} \text{ A}}{100} = 10^{-5} \text{ A} = 10 \text{ µA} \]

### Step 4: Calculate the Base Voltage (Vb)
Using Ohm's Law again, we can find the base voltage (Vb):
\[ Vb = Ib \times Rb = 10^{-5} \text{ A} \times 2000 \text{ Ω} = 2 \times 10^{-2} \text{ V} = 0.02 \text{ V} \]

### Step 5: Calculate the Voltage Gain (Av)
The voltage gain (Av) is given by the ratio of the collector voltage (Vc) to the base voltage (Vb):
\[ Av = \frac{Vc}{Vb} = \frac{3 \text{ V}}{0.02 \text{ V}} = 150 \]

### Step 6: Calculate the Power Gain (Ap)
The power gain (Ap) can be calculated using the formula:
\[ Ap = β \times Av = 100 \times 150 = 15000 \]

### Final Results
- Voltage Gain (Av) = 150
- Power Gain (Ap) = 15000