a common emitter amplifier gives an output of 3V for an input of 0.01 V. if current gain of the transistor is 100 and the input resistance is `10 k Omega`. Then the collector resistance is

Options

A. `30 kOmega`
B. `3 kOmega`
C. `1 kOmega`
D. `6 kOmega`

Answer

To find the collector resistance \( R_C \) of a common emitter amplifier given the output voltage, input voltage, current gain, and input resistance, we can follow these steps:

### Step 1: Identify the given values
- Output voltage \( V_0 = 3 \, V \)
- Input voltage \( V_i = 0.01 \, V \)
- Current gain \( \beta = 100 \)
- Input resistance \( R_{in} = 10 \, k\Omega = 10,000 \, \Omega \)

### Step 2: Calculate the voltage gain \( A_V \)
The voltage gain \( A_V \) is given by the formula:
\[ A_V = \frac{V_0}{V_i} \]
Substituting the values:
\[ A_V = \frac{3 \, V}{0.01 \, V} = 300 \]

### Step 3: Relate voltage gain to current gain and resistance gain
The voltage gain can also be expressed in terms of current gain and resistance gain:
\[ A_V = \beta \times \frac{R_L}{R_{in}} \]
Where \( R_L \) is the load resistance. Rearranging this gives:
\[ R_L = \frac{A_V \times R_{in}}{\beta} \]

### Step 4: Substitute the known values into the equation
Substituting the known values into the equation:
\[ R_L = \frac{300 \times 10,000 \, \Omega}{100} \]

### Step 5: Calculate \( R_L \)
Calculating \( R_L \):
\[ R_L = \frac{300 \times 10,000}{100} = 30,000 \, \Omega = 30 \, k\Omega \]

### Step 6: Identify the collector resistance
In a common emitter amplifier, the collector resistance \( R_C \) is typically equal to the load resistance \( R_L \). Therefore:
\[ R_C = R_L = 30 \, k\Omega \]

### Conclusion
The collector resistance \( R_C \) is \( 30 \, k\Omega \).