Question

Two coaxial coils are very close to each other and their mutual inductance is $5$ mH. If a current $50\sin 500r$ is passed in one of the coils then the peak value of induced e.m.f. in the secondary coil will be?

• A. $5000$V
• B. $500$V
• C. $150$V
• D. $125$V

Answer 1

The correct option is D $125$V

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

${\varphi }_2=M{i}_1$

M = mutual inductance

$i1$ = current in first coil

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

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

$EMF=M\frac{d{i}_1}{dt}$

now plug in value of current and mutual inductance

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

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

$EMF=125cos500t$

so above is the equation of induced EMF

so maximum value of induced EMF will be

$EM{F}_{max}=125volts$