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NEET PHYSICSMedium

A transistor is operated in a common emitter configuration at Vc=2 VV_c = 2 \text{ V} such that a change in the base current from 100 μA100 \text{ } \mu\text{A} to 300 μA300 \text{ } \mu\text{A} produces a change in the collector current from 10 mA10 \text{ mA} to 20 mA20 \text{ mA}. The current gain is:

A

75

B

100

C

25

D

50

Step-by-Step Solution

The AC current gain (βac\beta_{ac}) of a transistor in a common emitter configuration is defined as the ratio of the change in collector current (ΔIC\Delta I_C) to the change in base current (ΔIB\Delta I_B) at a constant collector-emitter voltage.

Given: Change in base current, ΔIB=300 μA100 μA=200 μA=0.2 mA\Delta I_B = 300 \text{ } \mu\text{A} - 100 \text{ } \mu\text{A} = 200 \text{ } \mu\text{A} = 0.2 \text{ mA} Change in collector current, ΔIC=20 mA10 mA=10 mA\Delta I_C = 20 \text{ mA} - 10 \text{ mA} = 10 \text{ mA}

Current gain, βac=ΔICΔIB\beta_{ac} = \frac{\Delta I_C}{\Delta I_B} βac=10 mA0.2 mA=50\beta_{ac} = \frac{10 \text{ mA}}{0.2 \text{ mA}} = 50

Therefore, the current gain is 50.

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