Easy MCQ +4 / -1 PYQ · JEE Mains 2025

Consider I1 and I2 are the currents flowing simultaneously in two nearby coils 1 & 2, respectively. If L1 = self inductance of coil 1, M12 = mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in coil 1 will be :

  1. A <p>e<sub>1</sub> = -L<sub>1</sub>$\frac{dI_2}{dt}$ - M<sub>12</sub>$\frac{dI_1}{dt}$</p>
  2. B <p>e<sub>1</sub> = -L<sub>1</sub>$\frac{dI_1}{dt}$ + M<sub>12</sub>$\frac{dI_2}{dt}$</p>
  3. C <p>e<sub>1</sub> = -L<sub>1</sub>$\frac{dI_1}{dt}$ - M<sub>12</sub>$\frac{dI_1}{dt}$</p>
  4. D <p>e<sub>1</sub> = -L<sub>1</sub>$\frac{dI_1}{dt}$ - M<sub>12</sub>$\frac{dI_2}{dt}$</p> Correct answer

Solution

<p>$$\begin{aligned} & \phi_1=\mathrm{L}_1 \mathrm{I}_1+\mathrm{M}_{12} \mathrm{I}_2 \\ & \varepsilon_1=-\frac{\mathrm{d} \phi_1}{\mathrm{dt}}=-\mathrm{L}_1 \frac{\mathrm{dI}_1}{\mathrm{dt}}-\mathrm{M}_{12} \frac{\mathrm{dI}}{\mathrm{dt}} \end{aligned}$$</p>

About this question

Subject: Physics · Chapter: Electromagnetic Induction · Topic: Self and Mutual Inductance

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