A transistor is operated in a common emitter configuration at $V_c = 2 ext{ V}$ such that a change in the ba

Question

A transistor is operated in a common emitter configuration at $V_c = 2 	ext{ V}$ such that a change in the base current from $100 	ext{ } \mu	ext{A}$ to $300 	ext{ } \mu	ext{A}$ produces a change in the collector current from $10 	ext{ mA}$ to $20 	ext{ mA}$. The current gain is:

Accepted Answer

The AC current gain ($\beta_{ac}$) of a transistor in a common emitter configuration is defined as the ratio of the 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, $\Delta I_B = 300 	ext{ } \mu	ext{A} - 100 	ext{ } \mu	ext{A} = 200 	ext{ } \mu	ext{A} = 0.2 	ext{ mA}$
Change in collector current, $\Delta I_C = 20 	ext{ mA} - 10 	ext{ mA} = 10 	ext{ mA}$

Current gain, $\beta_{ac} = \frac{\Delta I_C}{\Delta I_B}$
$$\beta_{ac} = \frac{10 	ext{ mA}}{0.2 	ext{ mA}} = 50$$

Therefore, the current gain is 50.

Step-by-Step Solution

Practice All PHYSICS Questions