Question

Two coaxial coils are very close to each other and their mutual inductance is 5 mh.if a current of 50 sin 500t is passed in one of the coils then the peak value of induced emf in the secondary coil will be

Answer 1

by the principle of mutual inductance we know that flux induced in coil 2 will depends on the current flowing in coil 1

$\phi_2 = Mi_1$

here

M = mutual inductance

i1 = current in first coil

now by Faraday's law induced EMF in 2nd coil will be

$\frac{d\phi}{dt} = EMF$

$EMF = M\frac{di_1}{dt}$

now plug in value of current and mutual inductance

$EMF = 5*10^{-3}\frac{d}{dt}(50 sin500t$

$EMF = 5*10^{-3}50*500*cos500t$

$EMF = 125 cos500t$

so above is the equation of induced EMF

so maximum value of induced EMF will be

$EMF_{max} = 125 volts$