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 determine the values of \( I_B \), \( I_C \), and \( \beta \), we analyze the given transistor circuit.

Step 1: Understanding the Circuit

• Input voltage \( V_i = 20\,\text{V} \)
• \( V_{BE} = 0\,\text{V} \)
• \( V_{CE} = 0\,\text{V} \)

Step 2: Base Current (\( I_B \))

Across base resistor \( R_B = 500\,\text{k}\Omega \):

\[ V_i = I_B R_B \]

\[ I_B = \frac{20}{500 \times 10^3} = 40\,\mu\text{A} \]

Step 3: Collector Current (\( I_C \))

Across collector resistor \( R_C = 4\,\text{k}\Omega \):

\[ I_C = \frac{20}{4 \times 10^3} = 5\,\text{mA} \]

Step 4: Current Gain (\( \beta \))

\[ \beta = \frac{I_C}{I_B} = \frac{5 \times 10^{-3}}{40 \times 10^{-6}} = 125 \]

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