What is the beta current ratio of a transistor?

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This question was previously asked in

RRB ALP CBT 2 Electronic Mechanic Previous Paper: Held on 23 Jan 2019 Shift 1

Answer 1

The common-emitter current gain (β) is the ratio of the transistor's collector current to the transistor's base current, i.e.

\(β = \frac{{{I_C}}}{{{I_B}}}\)

26 June 1

And the common base DC current gain (α) is a ratio of the transistor's collector current to the transistor's emitter current, i.e.

\(α = \frac{{{I_C}}}{{{I_E}}}\)

The transistor currents are related by the relation:

I_E = I_B + I_C

α can now be written as:

\(α = \frac{{{I_C}}}{{{I_B+I_C}}}\)

Dividing both the numerator and denominator by IB, we get:

\(α = \frac{{{I_C/I_B}}}{{{1+I_C/I_B}}}\)

Since \(β = \frac{{{I_C}}}{{{I_B}}}\)

\(α = \frac{β }{{β + 1}}\) 'or'

\(β = \frac{α }{{1-α}}\)