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In a certain transistor, the emitter current is 1.5 times larger as the collector current. If the emitter current is 15 mA, find the base current.
1. 15 mA
2. 5 mA
3. 4 mA
4. 6 mA

1 Answer

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Correct Answer - Option 2 : 5 mA

Concept:

In a transistor, emitter current (Ie)can be calculated as

I= Ib + Ic

Where,

Ib = base current

I= collector current

Common base current gain (α) is defined as the ratio of collector current to emitter current of a transistor.

\(\alpha = \dfrac{{{I_c}}}{{{I_e}}}\)

\(\alpha = \dfrac{β }{{β + 1}}\)

Common emitter current gain (β) is defined as the ratio of collector current to base current transistor.

\(β = \dfrac{{{I_c}}}{{{I_b}}}\)

\(β = \dfrac{\alpha }{{1 - \alpha }}\)

Calculation:

Given that, Ie = 1.5 Ic and Ie = 15 mA

\(\alpha = \dfrac{I_c}{I_e} = \dfrac{I_c}{1.5I_c}=0.666\)

\(β =\dfrac{\alpha}{1-\alpha}=\dfrac{0.666}{1-0.666}=2\)

I= Ib + Ic = Ib + βIb = (2 +1)Ib

\(\Rightarrow I_b=\dfrac{I_e}{\beta+1}=\dfrac{15}{2+1}mA=5 \;m A\)

Ib = 5 A

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