Question

In the circuit shown in the figure, the input voltage V_i is 20V, V_BE = 0 and V_CE = 0. The values of I_B , I_C and β are given by

• A. I_B=40μA, I_C=10mA, β=250
• B. I_B=20μA, I_C=5mA, β=250
• C. I_B=25μA, I_C=5mA, β=200
• D. I_B=40μA, I_C=5mA, β=125

Answer 1

The Correct Option is D

To solve this problem, we analyze the given transistor circuit.

Given:

• \( V_i = 20\,\text{V} \)
• \( V_{BE} = 0 \)
• \( V_{CE} = 0 \)
• \( R_B = 500\,\text{k}\Omega \)
• \( R_C = 4\,\text{k}\Omega \)

1. Base Current:
   \[ I_B = \frac{V_i}{R_B} = \frac{20}{500 \times 10^3} = 40\,\mu\text{A} \]
2. Collector Current:
   Since \( V_{CE} = 0 \), the full voltage appears across \( R_C \):
   \[ I_C = \frac{V_i}{R_C} = \frac{20}{4 \times 10^3} = 5\,\text{mA} \]
3. Current Gain:
   \[ \beta = \frac{I_C}{I_B} = \frac{5 \times 10^{-3}}{40 \times 10^{-6}} = 125 \]

Final Answer: \( I_B = 40\,\mu\text{A},\; I_C = 5\,\text{mA},\; \beta = 125 \)