The correct relation between $\alpha$ ( ratio of collector current to emitter current ) and $\beta$ ( ratio of collector current to base current) of a transistor is :

(B) $\alpha=\frac{\beta}{1+\beta}$

(A) $\beta=\frac{1}{1-\alpha}$

(C) $\alpha=\frac{\beta}{1-\alpha}$

(D) $\beta=\frac{\alpha}{1+\alpha}$

JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Semiconductors

The correct relation between

α

( ratio of collector current to emitter current ) and

β

( ratio of collector current to base current) of a transistor is :

Answer: (B)

The three terminal currents satisfy

I_{E} = I_{C} + I_{B}

. With

α = \frac{I _{C}}{I _{E}}

and

β = \frac{I _{C}}{I _{B}}

, dividing that relation throughout by

I_{C}

gives

\frac{1}{α} = 1 + \frac{1}{β} = \frac{β + 1}{β}

α = \frac{β}{1 + β}

JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Single correct option