Verified Solution • 2025–26 Session moderate

QJEEM24Ph6b2f: JEE Main 2024 Physics - Class 12 JEEM24Ph6b2f Solution: Two coils have mutual inductance . The current changes in the…

Two coils have mutual inductance 0.002 H0.002 \mathrm{~H} . The current changes in the first coil according to the relation i=i0sin⁡ωt\mathrm{i}=\mathrm{i}_0 \sin \omega \mathrm{t} , where i0=5 A\mathrm{i}_0=5 \mathrm{~A} and ω=50π\omega=50 \pi rad/s. The maximum value of emf in the second coil is πα V\frac{\pi}{\alpha} \mathrm{~V} . The value of α\alpha is _______.

Step-by-Step Verified Solution

amp;ϕ=Mi=Mi0sin⁡ωtamp;EMF=−Mdidt=−0.002(i0ωcos⁡ωt)amp;EMFmax⁡=i0ω(0.002)=(5)(50π)(0.002)amp;EMFmax⁡=π2 V\begin{aligned}& \phi=\mathrm{Mi}=\mathrm{Mi}_0 \sin \omega \mathrm{t} \\& \mathrm{EMF}=-\mathrm{M} \frac{\mathrm{di}}{\mathrm{dt}}=-0.002\left(\mathrm{i}_0 \omega \cos \omega \mathrm{t}\right) \\& \mathrm{EMF}_{\max }=\mathrm{i}_0 \omega(0.002)=(5)(50 \pi)(0.002) \\& \mathrm{EMF}_{\max }=\frac{\pi}{2} \mathrm{~V}\end{aligned}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring