Two coils have a mutual inductance 5 × 10⁻³ H. The current changes in the first coil according to the equation I₁ = I₀ sin ω t where I₀ = 10 A and ω = 100π rad/s. What is the value of the maximum e.m.f. in the coil? (a) 2π V (b) 3π V (c) 4π V (d) 5π V

Answer: (d). e = -M(dI₁)/(dt) = -MI₀ωcos ω t, so emax = MI₀ω emax = 5 × 10⁻³ × 10 × 100π = 5π V So the answer is (d) 5π V.

Two coils have a mutual inductance 5 × 10⁻³ H. The current changes in… | MHT CET 2024 (9 May, Shift 1)

Q26MHT CET 2024 · 9 MAY · SHIFT 1Easy

Mutual Inductance

Two coils have a mutual inductance $5 \times 10^{-3}\text{ H}$ . The current changes in the first coil according to the equation $I_1 = I_0 \sin \omega t$ where $I_0 = 10\text{ A}$ and $\omega = 100\pi\text{ rad/s}$ . What is the value of the maximum e.m.f. in the coil?

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Answer: (d)

$e = -M\dfrac{dI_1}{dt} = -MI_0\omega\cos\omega t$ , so $e_{max} = MI_0\omega$
$e_{max} = 5 \times 10^{-3} \times 10 \times 100\pi = 5\pi\text{ V}$
So the answer is (d) $5\pi\text{ V}$ .

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Mutual Inductance question from MHT CET 2024 (9 May, Shift 1)

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