Question

In a certain transistor, the emitter current is 1.04 times the collector current. If the emitter current is 12 mA, calculate the base current.
1. 462 μA
2. 11.538 mA
3. 462 mA
4. 11.538 μA

Answer 1

Correct Answer - Option 1 : 462 μA

Concept:

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

Ie = Ib + Ic

Where,

Ib = base current

Ic = 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 = 1.04 I_c and Ie = 12 mA

\(\alpha = \dfrac{I_c}{I_e} = \dfrac{I_c}{1.04I_c}=0.9615\)

\(β =\dfrac{\alpha}{1-\alpha}=\dfrac{0.9615}{1-0.9615}=25\)

Ie = Ib + Ic = I_b + βI_b = (β +1)I_b

\(\Rightarrow I_b=\dfrac{I_e}{\beta+1}=\dfrac{12}{25+1}mA=461.53 \;μ A\)

I_b ≈ 462 μA