Q118 / 150 · MHT CET 2020 (16 Oct Shift 1) · Physics

A coil of 'n' turns and resistance 'R' $\Omega$ is connected in series with a resistance $\frac{\mathrm{R}}{2}$ The combination is moved for time 't' second through magnetic flux $\phi_{1}$ to $\phi_{2}$. The induced current in the circuit is

  • Correct answer
    A
    $\frac{2 n\left(\phi_{1}-\phi_{2}\right)}{3 R t}$
  • B
    $\frac{n\left(\phi_{1}-\phi_{2}\right)}{3 R t}$
  • C
    $\frac{n\left(\phi_{1}-\phi_{2}\right)}{R t}$
  • D
    $\frac{2 n\left(\phi_{1}-\phi_{2}\right)}{R t}$

Solution

Total resistance $=\mathrm{R}+\frac{\mathrm{R}}{2}=\frac{3 \mathrm{R}}{2}$ $\mathrm{i}_{\text {induced }}=\frac{\mathrm{e}_{\text {induced }}}{\frac{3 \mathrm{R}}{2}}=\frac{\frac{\mathrm{d} \phi}{\mathrm{dt}}}{\frac{3 \mathrm{R}}{2}}=\frac{2 \mathrm{n}}{3 \mathrm{Rt}} \frac{\left(\phi_{1}-\phi_{2}\right)}{}$

Hence, the correct answer is option: 'A'.

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