Question

In a common emitter transistor, \( \beta = 100 \), \( R_c = 2\,\text{k}\Omega \), and the output voltage is \(2\,\text{V}\). If \( R_b = 1\,\text{k}\Omega \), find the input voltage.

• A. \(0.02\,\text{V}\)
• B. \(0.02\,\text{V}\)
• C. \(0.1\,\text{V}\)
• D. \(0.2\,\text{V}\)

Hint:

For common emitter amplifiers, remember the gain formula \( A_v = \beta \frac{R_c}{R_b} \). Then use \( A_v = \frac{V_{out}}{V_{in}} \) to find the required voltage.

Answer 1

The Correct Option is B

Concept: The voltage gain of a common emitter transistor amplifier is given by: \[ A_v = \beta \frac{R_c}{R_b} \] Also, \[ A_v = \frac{V_{out}}{V_{in}} \] These relations allow us to determine the input voltage when the output voltage and gain are known.

Step 1: Calculate the voltage gain. \[ A_v = \beta \frac{R_c}{R_b} \] \[ A_v = 100 \times \frac{2}{1} \] \[ A_v = 200 \]

Step 2: Use the gain relation. \[ A_v = \frac{V_{out}}{V_{in}} \] \[ 200 = \frac{2}{V_{in}} \]

Step 3: Solve for the input voltage. \[ V_{in} = \frac{2}{200} \] \[ V_{in} = 0.01\,\text{V} \]