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NEET PHYSICSMedium

A transistor is operated in a common emitter configuration at constant collector voltage Vc=1.5 VV_c = 1.5 \text{ V} such that a change in the base current from 100 μA100 \text{ } \mu\text{A} to 150 μA150 \text{ } \mu\text{A} produces a change in the collector current from 5 mA5 \text{ mA} to 10 mA10 \text{ mA}. The current gain (β\beta) is:

A

67

B

75

C

100

D

50

Step-by-Step Solution

The current gain (β\beta) in a common emitter configuration is defined as the ratio of 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=150 μA100 μA=50 μA=50×106 A\Delta I_B = 150 \text{ } \mu\text{A} - 100 \text{ } \mu\text{A} = 50 \text{ } \mu\text{A} = 50 \times 10^{-6} \text{ A} Change in collector current, ΔIC=10 mA5 mA=5 mA=5×103 A\Delta I_C = 10 \text{ mA} - 5 \text{ mA} = 5 \text{ mA} = 5 \times 10^{-3} \text{ A}

Current gain, β=ΔICΔIB\beta = \frac{\Delta I_C}{\Delta I_B} β=5×103 A50×106 A=5000×10650×106=100\beta = \frac{5 \times 10^{-3} \text{ A}}{50 \times 10^{-6} \text{ A}} = \frac{5000 \times 10^{-6}}{50 \times 10^{-6}} = 100

Therefore, the current gain is 100.

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