Question

In the given circuit, the input voltage across base resistance 10V. If base-emitter and collector-emitter voltages are zero, then the current amplification factor of the transistor is:

• A. 25
• B. 50
• C. 100
• D. 125

Hint:

Current amplification factor $\beta = \frac{I_C}{I_B}$. Calculate base current using $I_B = \frac{V_{{in}} - V_{{BE}}}{R_B}$ and collector current using $I_C = \frac{V_{{CC}} - V_{{CE}}}{R_C}$.

Answer 1

The Correct Option is C

Given: $V_{{BE}} = 0$, $V_{{CE}} = 0$, $V_{{in}} = 10$ V, $R_B = 400$ k$\Omega$, $R_C = 4$ k$\Omega$.
Base current $I_B = \frac{V_{{in}} - V_{{BE}}}{R_B} = \frac{10 - 0}{400 \times 10^3} = \frac{10}{400 \times 10^3} = 25 \times 10^{-6}$ A.
Collector current: Since $V_{{CE}} = 0$, the collector voltage is the same as the emitter (ground), so $I_C = \frac{V_{{CC}} - V_{{CE}}}{R_C} = \frac{10 - 0}{4 \times 10^3} = 2.5 \times 10^{-3}$ A.
Current amplification factor $\beta = \frac{I_C}{I_B} = \frac{2.5 \times 10^{-3}}{25 \times 10^{-6}} = 100$.