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

The current gain $\beta$ tells us how strongly a small wiggle in base current controls the collector current in the common-emitter configuration. It is defined as $\beta = \Delta I_C / \Delta I_B$.

Convert everything to the same unit first. The base current change is $\Delta I_B = (80 - 30)\ \mu\text{A} = 50\ \mu\text{A}$, which equals $50 \times 10^{-6}$ A. The collector current change is $\Delta I_C = (3.5 - 1.0)\ \text{mA} = 2.5\ \text{mA}$, which equals $2.5 \times 10^{-3}$ A.

Now divide the two:
\[ \beta = \frac{2.5 \times 10^{-3}}{50 \times 10^{-6}} = \frac{2.5 \times 10^{-3}}{5.0 \times 10^{-5}} = 50. \]
So a 50 microamp nudge at the base produces a 2.5 milliamp swing at the collector, a gain of fifty.
\[\boxed{\beta = 50}\]