Q158 / 160 · TS EAMCET 2023 (12 May Shift 2) · Physics
If the ratio of electron and hole currents in a semiconductor is $\frac{7}{4}$ and the ratio of drift velocities of electrons and holes is $\frac{5}{4}$, then ratio of concentrations of electrons and holes will be
- A$5: 7$
- Correct answerB$7: 5$
- C$5: 9$
- D$9: 5$
Solution
Ratio of electron \& Hole current,
$$
\frac{\mathrm{I}_{\mathrm{e}}}{\mathrm{I}_{\mathrm{n}}}=\frac{7}{4}
$$
Ratio of velocities, $\frac{v_e}{v_n}=\frac{5}{4}$
Current is given by: $\mathrm{I}=\mathrm{ne}_{\mathrm{d}}$.
$$
\mathrm{n}=\frac{\mathrm{I}}{\mathrm{eAV}}
$$
Ratio of concentration of electrons \& holes:
$$
\frac{\mathrm{n}_{\mathrm{e}}}{\mathrm{n}_{\mathrm{n}}}=\frac{\mathrm{I}_{\mathrm{e}}}{\mathrm{ev}_{\mathrm{e}} \mathrm{A}} \times \frac{\mathrm{ev}_{\mathrm{n}} \mathrm{A}}{\mathrm{I}_{\mathrm{n}}}=\frac{7}{4} \times \frac{4}{5}=\frac{7}{5}
$$
Hence, the correct answer is option: 'B'.