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 :

Correct answer: D. α = (β)/(1 + β) α = I _ C I _ E , β = I _ C I _ B I _ E = I _ B + I _ C α = I _ C I _ B + I _ C = 1 I _ B I _ C + 1 α = (1)/((1)/(β) + 1) α = (β)/(1 + β)

JEE Main 202118 MarchEvening Shift

Exam: JEE Main
Year: 2021
Date: 18 March
Shift: Evening Shift
Subject: Physics
Chapter: Semiconductors

JEE Main 2021 · 18 March · Evening Shift · Physics · Semiconductors

The correct relation between α (ratio of collector current to...

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 :

Options

A $\beta = \dfrac{\alpha}{1 + \alpha}$
B $\alpha = \dfrac{\beta}{1 - \alpha}$
C $\beta = \dfrac{1}{1 - \alpha}$
D $\alpha = \dfrac{\beta}{1 + \beta}$

Correct answer

D. $\alpha = \dfrac{\beta}{1 + \beta}$

Step-by-step solution

$\alpha = \dfrac{{I}_{C}}{{I}_{E}}, \beta = \dfrac{{I}_{C}}{{I}_{B}}$

${I}_{E} = {I}_{B} + {I}_{C}$

$\alpha = \dfrac{{I}_{C}}{{I}_{B} + {I}_{C}} = \dfrac{1}{\dfrac{{I}_{B}}{{I}_{C}} + 1}$

$\alpha = \dfrac{1}{\dfrac{1}{\beta} + 1}$

$\alpha = \dfrac{\beta}{1 + \beta}$

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