A transistor is used as a common emitter amplifier with a load resistance of `2kOmega`. The input resistance is `150Omega.` Base current is changed by `20muA` which results in change in collector current by 1.5 mA. The voltage gain of the amplifier is

Options

A. 900
B. 1000
C. 1100
D. 1200

Answer

To find the voltage gain of the common emitter amplifier, we can use the following formula:

\[ A_v = \beta \times \frac{R_{out}}{R_{in}} \]

Where:
- \(A_v\) is the voltage gain,
- \(\beta\) is the current gain,
- \(R_{out}\) is the output resistance (load resistance),
- \(R_{in}\) is the input resistance.

### Step 1: Calculate the Current Gain (\(\beta\))
The current gain \(\beta\) can be calculated using the formula:

\[ \beta = \frac{I_C}{I_B} \]

Where:
- \(I_C\) is the change in collector current,
- \(I_B\) is the change in base current.

Given:
- \(I_C = 1.5 \, \text{mA} = 1.5 \times 10^{-3} \, \text{A}\)
- \(I_B = 20 \, \mu\text{A} = 20 \times 10^{-6} \, \text{A}\)

Substituting the values:

\[ \beta = \frac{1.5 \times 10^{-3}}{20 \times 10^{-6}} = \frac{1.5}{20} \times 10^{3} = 0.075 \times 10^{3} = 75 \]

### Step 2: Identify the Output and Input Resistance
Given:
- \(R_{out} = 2 \, k\Omega = 2000 \, \Omega\)
- \(R_{in} = 150 \, \Omega\)

### Step 3: Calculate the Voltage Gain (\(A_v\))
Now we can substitute the values of \(\beta\), \(R_{out}\), and \(R_{in}\) into the voltage gain formula:

\[ A_v = \beta \times \frac{R_{out}}{R_{in}} = 75 \times \frac{2000}{150} \]

Calculating the fraction:

\[ \frac{2000}{150} = \frac{2000 \div 50}{150 \div 50} = \frac{40}{3} \approx 13.33 \]

Now substituting back into the voltage gain equation:

\[ A_v = 75 \times 13.33 \approx 999.75 \]

### Final Step: Approximate the Result
Thus, the voltage gain \(A_v\) can be approximated as:

\[ A_v \approx 1000 \]

### Conclusion
The voltage gain of the amplifier is approximately \(1000\).

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