Question

In a transistor amplifier, a change of 0.2 mA in the base current causes a change of 5 mA in the collector current. If input resistance is \(2 \text{k}\Omega\) and voltage gain is 75, the load resistance used in the circuit is

• A. \(4 \text{k}\Omega\)
• B. \(6 \text{k}\Omega\)
• C. \(8 \text{k}\Omega\)
• D. \(2 \text{k}\Omega\)

Hint:

Voltage gain equals current gain times load over input resistance.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Current gain \(\beta = \dfrac{\Delta I_C}{\Delta I_B}\) and voltage gain \(A_v = \beta\,\dfrac{R_L}{R_{in}}\).

Step 2: Current gain:
\[ \beta = \frac{5\ \text{mA}}{0.2\ \text{mA}} = 25 \]

Step 3: Load resistance:
\[ 75 = 25\times\frac{R_L}{2\ \text{k}\Omega} \Rightarrow R_L = \frac{75\times2}{25} = 6\ \text{k}\Omega \]

Step 4: Check:
Option (B). With 4 k\(\Omega\) the gain would be 50, with 8 k\(\Omega\) it would be 100, and with 2 k\(\Omega\) it would be 25.

Final Answer:
Beta is 25, and 75 = 25 times R_L / 2 k. \[ \boxed{\text{(B) }6\ \text{k}\Omega} \]