A 50 Hz a.c current of peak value 2 A flows through one of the pair of coils. If the mutual inductan

Question

A 50 Hz a.c current of peak value 2 A flows through one of the pair of coils. If the mutual inductance between the pair of coils is 150 mH , then the peak value of voltage induced in the second coil is\

Professor PC Thomas Classes · Answer

The current flows through the coil I is $I_{1}=I_{0} \sin \omega t$ Where $\mathrm{I}_{0}$ is the peak value of current\ Magnetic flux linked with the coil 2 is\ $\phi_{2}=\mathrm{MI}_{1}=\mathrm{MI}_{0} \sin \omega \mathrm{t}$\ Where M is the mutual inductance between the two coils\ The magnitude of induced emf in coil 2 is\ $\left|\varepsilon_{2}ight|=\frac{\mathrm{d} \phi_{2}}{\mathrm{dt}}=\frac{\mathrm{d}}{\mathrm{dt}}\left(\mathrm{MI}_{0} \sin \omega \mathrm{t}ight)$\ $=\mathrm{MI}_{0} \omega \cos \omega \mathrm{t}$\ $	herefore$ Peak value of voltage induced in the coil 2 is $=\mathrm{MI}_{0} \omega$\ $=150 	imes 10^{-3} 	imes 2 	imes 2 \pi 	imes 50=30 \pi \mathrm{~V}$\