A transistor is operated in common emitter configuration at $V_{c}=3 V$ such that a change in the base current from 50 µA to 250 µA produces a change in the collector current from 5 mA to 20 mA. The current gain is:

75

The correct answer is Option (1) → 75

The current gain (β) of a transistor in the common emitter configuration -

$β=\frac{ΔI_C}{ΔI_B}$

where,

$ΔI_C$ → Change in collector current

$ΔI_B$ → Change in base current

$∴ ΔI_C=20mA-5mA=15mA$

$ΔI_C=250μA-50μA=200μA$

$=0.2mA$

$∴β=\frac{15}{0.2}=75$