Correct Answer - Option 2 : 5 mA
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 = 1.5 Ic and Ie = 15 mA
\(\alpha = \dfrac{I_c}{I_e} = \dfrac{I_c}{1.5I_c}=0.666\)
\(β =\dfrac{\alpha}{1-\alpha}=\dfrac{0.666}{1-0.666}=2\)
Ie = 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