A transistor is operated in a common emitter configuration at constant collector voltage $V_c = 1.5 ext{ V}$

Question

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

Accepted Answer

The current gain ($\beta$) in a common emitter configuration is defined as the ratio of change in collector current ($\Delta I_C$) to the change in base current ($\Delta I_B$) at a constant collector-emitter voltage.

Given:
Change in base current, $\Delta I_B = 150 	ext{ } \mu	ext{A} - 100 	ext{ } \mu	ext{A} = 50 	ext{ } \mu	ext{A} = 50 	imes 10^{-6} 	ext{ A}$
Change in collector current, $\Delta I_C = 10 	ext{ mA} - 5 	ext{ mA} = 5 	ext{ mA} = 5 	imes 10^{-3} 	ext{ A}$

Current gain, $\beta = \frac{\Delta I_C}{\Delta I_B}$
$$\beta = \frac{5 	imes 10^{-3} 	ext{ A}}{50 	imes 10^{-6} 	ext{ A}} = \frac{5000 	imes 10^{-6}}{50 	imes 10^{-6}} = 100$$

Therefore, the current gain is 100.

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