In a study of transistor as an amplifier, the ratio of collector current to emitter current is $0.98 .$ The…

In a study of transistor as an amplifier, the ratio of collector current to emitter current is $0.98 .$ The collector current is $3 \mathrm{~mA}$, then base current will be approximately
  1. $6 \mathrm{~mA}$
  2. $60 \mathrm{~mA}$
  3. $6 \mu \mathrm{A}$
  4. $60 \mu \mathrm{A}$

Solution

$\frac{i_{c}}{i_{c}}=0.98 \quad i_{c}=3 \mathrm{~mA} \quad i_{b}=?$ $\frac{i_{c}}{i_{c}+i_{b}}=0.98=\frac{98}{100} \Rightarrow \frac{i_{c}+i_{b}}{i_{c}}=\frac{100}{98}$ $1+\frac{\mathrm{i}_{\mathrm{b}}}{\mathrm{i}_{\mathrm{c}}}=\frac{100}{98} \quad \therefore \frac{\mathrm{i}_{\mathrm{b}}}{\mathrm{i}_{\mathrm{c}}}=\frac{2}{98} \quad \therefore \mathrm{i}_{\mathrm{b}}=3 \times \frac{2}{98}=\frac{3}{49} \mathrm{~mA}$ $=\frac{3000}{49} \mu \mathrm{A}=61.22 \mu \mathrm{A} \approx 60 \mu \mathrm{A}$

Asked in: MHT CET 2020 (20 Oct Shift 2)

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