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  4. A transistor is operated in common emitter configuration at constant collector voltage VC=1.5 V such that a change in the base current from 100 μ A to 150 μ A produces a change in the collector current from 5 mA to 10 mA. The current gain ( β ) is

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Q. A transistor is operated in common emitter configuration at constant collector voltage $ {{V}_{C}}=1.5\,V $ such that a change in the base current from 100 $ \mu A $ to 150 $ \mu A $ produces a change in the collector current from 5 mA to 10 mA. The current gain ( $ \beta $ ) is

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Solution:

AC current gain $ \beta $ is defined as the ratio of the collector to the base current at constant collector voltage, $ \beta =\left( \frac{\Delta {{i}_{C}}}{\Delta {{i}_{B}}} \right){{V}_{c}} $ Given $ \Delta {{i}_{C}}=10\,mA-5mA=5mA $ $ \Delta {{i}_{B}}=150\,\mu A-100\mu A=50\,\mu A $ $ \therefore $ $ \beta =\frac{5}{50\times {{10}^{-3}}}=100 $