Question

When the base current in a transistor is changed from 30 µA to 80 µA, the collector current is changed from 1.0 mA to 3.5 mA. Then, the current gain \(\beta\) is:

• A. 100
• B. 200
• C. 75
• D. 50

Hint:

beta = change in collector current divided by change in base current. Keep units consistent: 2.5 mA over 50 microamp.

Answer 1

The Correct Option is D

Step 1: The common-emitter AC current gain is the ratio of the change in collector current to the change in base current at constant collector-emitter voltage:
\[ \beta = \frac{\Delta I_C}{\Delta I_B}. \]

Step 2: Compute the two changes:
\[ \Delta I_C = 3.5\ \text{mA} - 1.0\ \text{mA} = 2.5\ \text{mA} = 2500\ \mu\text{A}, \]
\[ \Delta I_B = 80\ \mu\text{A} - 30\ \mu\text{A} = 50\ \mu\text{A}. \]

Step 3: Divide:
\[ \beta = \frac{2500\ \mu\text{A}}{50\ \mu\text{A}} = 50. \]
\[\boxed{\beta = 50}\]