Question:
Two coils have mutual inductance 0.005 H. The current changes in the first coil according to equation \(I = I_0 \sin \omega t\), where \(I_0 = 10\text{ A}\) and \(\omega = 100\pi\text{ rad/s}\). The maximum value of emf in the second coil is
Two coils have mutual inductance 0.005 H. The current changes in the first coil according to equation \(I = I_0 \sin \omega t\), where \(I_0 = 10\text{ A}\) and \(\omega = 100\pi\text{ rad/s}\). The maximum value of emf in the second coil is
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\(E_{\text{max}} = M I_0 \omega\) for sinusoidal current.
Updated On: Apr 20, 2026
- \(12\pi\)
- \(8\pi\)
- \(5\pi\)
- \(2\pi\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
Induced emf in secondary: \(E = -M\frac{dI}{dt}\).
Step 2: Detailed Explanation:
\(I = 10\sin(100\pi t)\)
\(\frac{dI}{dt} = 10 \times 100\pi \cos(100\pi t) = 1000\pi \cos(100\pi t)\)
\(E_{\text{max}} = M \times \left(\frac{dI}{dt}\right)_{\text{max}} = 0.005 \times 1000\pi = 5\pi \text{ V}\).
Step 3: Final Answer:
\(\boxed{5\pi}\)
Induced emf in secondary: \(E = -M\frac{dI}{dt}\).
Step 2: Detailed Explanation:
\(I = 10\sin(100\pi t)\)
\(\frac{dI}{dt} = 10 \times 100\pi \cos(100\pi t) = 1000\pi \cos(100\pi t)\)
\(E_{\text{max}} = M \times \left(\frac{dI}{dt}\right)_{\text{max}} = 0.005 \times 1000\pi = 5\pi \text{ V}\).
Step 3: Final Answer:
\(\boxed{5\pi}\)
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