A common emitter amplifier gives an output of 3 V for an input of 0.01 V. If `beta` of the resistance is 100 and the input resistance is `1 kOmega`. then the collector resistance is

Options

A. `3 kOmega`
B. `30 kOmega`
C. `1 kOmega`
D. `5 kOmega`

Explanation

To find the collector resistance \( R_C \) of a common emitter amplifier given the output voltage \( V_0 \), input voltage \( V_i \), current gain \( \beta \), and input resistance \( R_i \), we can follow these steps:

### Step-by-Step Solution

1. **Identify the Given Values:**
- Output Voltage, \( V_0 = 3 \, \text{V} \)
- Input Voltage, \( V_i = 0.01 \, \text{V} \)
- Current Gain, \( \beta = 100 \)
- Input Resistance, \( R_i = 1 \, \text{k}\Omega = 1000 \, \Omega \)

2. **Calculate the Voltage Gain:**
The voltage gain \( A_V \) of the amplifier can be calculated using the formula:
\[ A_V = \frac{V_0}{V_i} \]
Substituting the given values:
\[ A_V = \frac{3 \, \text{V}}{0.01 \, \text{V}} = 300 \]

3. **Relate Voltage Gain to Current Gain and Resistance Gain:**
The voltage gain can also be expressed in terms of the current gain \( \beta \) and the resistance gain \( \frac{R_0}{R_i} \):
\[ A_V = \beta \cdot \frac{R_0}{R_i} \]
Substituting the known values:
\[ 300 = 100 \cdot \frac{R_0}{1000} \]

4. **Solve for \( R_0 \):**
Rearranging the equation to solve for \( R_0 \):
\[ \frac{R_0}{1000} = \frac{300}{100} \Rightarrow \frac{R_0}{1000} = 3 \]
Therefore:
\[ R_0 = 3 \cdot 1000 = 3000 \, \Omega = 3 \, \text{k}\Omega \]

5. **Conclusion:**
The collector resistance \( R_C \) is equal to \( R_0 \), which we have calculated to be:
\[ R_C = 3 \, \text{k}\Omega \]

### Final Answer:
The collector resistance \( R_C \) is \( 3 \, \text{k}\Omega \).

---