Question

The power gain of a transistor operating in common emitter configuration is 32,000. If the input and output resistances of the circuit are 1200 \( \Omega \) and 6000 \( \Omega \) respectively, then the current gain is:

• A. 8000
• B. 800
• C. 80
• D. 6400

Hint:

For calculating current gain from power gain, remember the relationship between resistance ratios and current gain squared.

Answer 1

The Correct Option is C

Step 1: The power gain \( P_g \) is related to the current gain \( \beta \) and the resistances \( R_{\text{in}} \) and \( R_{\text{out}} \) by the formula: \[ P_g = \beta^2 \frac{R_{\text{out}}}{R_{\text{in}}} \] Substituting the given values: \[ 32,000 = \beta^2 \frac{6000}{1200} \] \[ 32,000 = \beta^2 \times 5 \] \[ \beta^2 = \frac{32,000}{5} = 6400 \] \[ \beta = \sqrt{6400} = 80 \] Thus, the current gain is 80.