Question

The input resistan ce o f a silicon transistor is $100 \,\Omega$ B a se current is changed by $40 \,\mu A$ which results in a change in collector currently by $2 \,m A$ . This transistor is used as a comm on emitter amplifier with a load resistance o f $4 \,k\Omega$ The voltage gain o f the amplifier is

• A. 2000
• B. 3000
• C. 4000
• D. 1000

Answer 1

The Correct Option is A

To determine the voltage gain of the common emitter amplifier, we need to calculate the current gain and use it to find the voltage gain.

Let's go step by step: 

1. The given input resistance is \(100 \, \Omega\).
2. Base current change, \(\Delta I_b = 40 \, \mu A = 40 \times 10^{-6} \, A\).
3. Collector current change, \(\Delta I_c = 2 \, mA = 2 \times 10^{-3} \, A\).

Calculate the current gain \((\beta)\) of the transistor:

\(\beta = \frac{\Delta I_c}{\Delta I_b} = \frac{2 \times 10^{-3} \, A}{40 \times 10^{-6} \, A} = 50\).

The load resistance \((R_L)\) is given as \(4 \, k\Omega = 4000 \, \Omega\).

The voltage gain \((A_v)\) of the amplifier is calculated with the formula:

\(A_v = -\beta \times \frac{R_L}{R_{in}}\),

where \(R_{in} = 100 \, \Omega\) is the input resistance.

 

Substitute the given values:

\(A_v = -50 \times \frac{4000 \, \Omega}{100 \, \Omega} = -50 \times 40 = -2000\).

The magnitude of the voltage gain is \(2000\).

Therefore, the correct answer is 2000.