Mutual Inductance
Two coupled coils have a mutual inductance of 0.2 H. If the current in the primary coil changes steadily at the rate of 30 A/s, what EMF is induced in the secondary coil?
Select the correct option:
Solution
6 V
Mutual inductance describes how a changing current in one coil drives an EMF in a neighbouring coil by linking part of its flux through the second winding, quantified by (\varepsilon_2 = -M,\dfrac{dI_1}{dt}). The magnitude of the secondary EMF therefore equals the mutual inductance multiplied by the rate at which the primary current changes. Substituting (M = 0.2) H and (dI_1/dt = 30) A/s gives (|\varepsilon_2| = 0.2 \times 30 = 6) V. The option 3 V wrongly halves the rate of change. The option 0.6 V misplaces a decimal and effectively uses 3 A/s. The option 12 V doubles the mutual inductance. This is the coupling relation NCERT introduces using two concentric solenoids, where the same (M) governs induction in either direction. A unit check confirms H·(A/s) reduces to volts, and a few volts is a realistic transformer-style coupling output for a modest current slew rate; the negative sign merely encodes Lenz's-law opposition and does not affect the magnitude requested.
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About This Question
- Subject
- physics
- Chapter
- electromagnetic induction and alternating currents
- Topic
- mutual inductance
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
6 V
Mutual inductance describes how a changing current in one coil drives an EMF in a neighbouring coil by linking part of its flux through the second winding, quantified by (\varepsilon_2 = -M,\dfrac{dI_1}{dt}). The magnitude of the secondary EMF therefore equals the mutual inductance multiplied by the rate at which the primary current changes. Substituting (M = 0.2) H and (dI_1/dt = 30) A/s gives (|\varepsilon_2| = 0.2 \times 30 = 6) V. The option 3 V wrongly halves the rate of change. The option 0.6 V misplaces a decimal and effectively uses 3 A/s. The option 12 V doubles the mutual inductance. This is the coupling relation NCERT introduces using two concentric solenoids, where the same (M) governs induction in either direction. A unit check confirms H·(A/s) reduces to volts, and a few volts is a realistic transformer-style coupling output for a modest current slew rate; the negative sign merely encodes Lenz's-law opposition and does not affect the magnitude requested.
This easy difficulty physics question is from the chapter electromagnetic induction and alternating currents, covering the topic of mutual inductance. It appeared in the 2025 exam.
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