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JEE Main 2004
Exam
JEE Main
Year
2004
Subject
Physics
Chapter
Electromagnetic Induction

JEE Main 2004 · Physics · Electromagnetic Induction

A coil having n turns and resistance 4 R . This combination is...

A coil having nn turns and resistance 4RΩ4 \mathrm{R} \Omega. This combination is moved in time tt seconds from a magnetic field W1W_1 weber to W2W_2 weber. The induced current in the circuit is

Options

  1. A−W2−W15Rnt-\frac{W_2-W_1}{5 R n t}
  2. B−(W2−W1)5Rt-\frac{\left(\mathrm{W}_2-\mathrm{W}_1\right)}{5 \mathrm{Rt}}
  3. C−W2−W1 Rnt -\frac{W_2-W_1}{\text{ Rnt }}
  4. D-\frac{\mathrm{n}\left(\mathrm{W}_2-\mathrm{W}_1\right)}{\mathrm{Rt}}

Correct answer

B. −(W2−W1)5Rt-\frac{\left(\mathrm{W}_2-\mathrm{W}_1\right)}{5 \mathrm{Rt}}

Step-by-step solution

\mathrm{I}=-\frac{\mathrm{I}}{\mathrm{R}^{\prime}} \frac{\mathrm{d} \phi}{\mathrm{dt}} or, I =−1R′n[W2−W1t2−t1]=-\frac{1}{R^{\prime}} \mathrm{n}\left[\frac{\mathrm{W}_2-\mathrm{W}_1}{\mathrm{t}_2-\mathrm{t}_1}\right] ( W1W_1 and W2W_2 are not the magnetic field, but the values of flux associated with one turn of coil) I=−1(R+4R)n(W2−W1)tI=\frac{-1}{(R+4 R)} \frac{n\left(W_2-W_1\right)}{t} or, I=−n(W2−W1)5Rt\mathrm{I}=-\frac{\mathrm{n}\left(\mathrm{W}_2-\mathrm{W}_1\right)}{5 \mathrm{Rt}}
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