Question:
A current \(i=10\,\sin (100\pi t)\) A is passed in first coil, which induces a maximum e.m.f. \(5\pi\) V in second coil. The mutual inductance between the coils is
A current \(i=10\,\sin (100\pi t)\) A is passed in first coil, which induces a maximum e.m.f. \(5\pi\) V in second coil. The mutual inductance between the coils is
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Peak induced emf equals \(M\) times the peak rate of change of current.
Updated On: Nov 12, 2026
- \(10\) mH
- \(15\) mH
- \(25\) mH
- \(5\) mH
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
The induced emf in the second coil is \(\varepsilon=M\dfrac{di}{dt}\).
Step 2: Peak Rate of Change
\(i=10\sin(100\pi t)\Rightarrow\dfrac{di}{dt}=1000\pi\cos(100\pi t)\), so the maximum is \(1000\pi\) A/s.
Step 3: Calculation
\(5\pi=M\times 1000\pi\Rightarrow M=5\times 10^{-3}\) H
Step 4: Compare the options
\(M=5\) mH, option (D).
Final Answer:
The mutual inductance is 5 mH. \[ \boxed{\text{(D) }5\text{ mH}} \]
The induced emf in the second coil is \(\varepsilon=M\dfrac{di}{dt}\).
Step 2: Peak Rate of Change
\(i=10\sin(100\pi t)\Rightarrow\dfrac{di}{dt}=1000\pi\cos(100\pi t)\), so the maximum is \(1000\pi\) A/s.
Step 3: Calculation
\(5\pi=M\times 1000\pi\Rightarrow M=5\times 10^{-3}\) H
Step 4: Compare the options
\(M=5\) mH, option (D).
Final Answer:
The mutual inductance is 5 mH. \[ \boxed{\text{(D) }5\text{ mH}} \]
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