Question

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

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

Answer 1

The correct option is D $125V$

By the principle of mutual inductance we know that flux induced in coil2 will depend on the current flowing in coil1

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

Here

M=Mutual inductance

$i_1$=current in 1st coil

Now by Faraday's law induced emf in 2nd coil will be

$\frac{d\Phi }{dt}=emf$

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

Now put value of current and mutual inductance

$emf=(5\times {10}^{-3})\frac{d\left(50\sin 500t\right)}{dt}$

$emf=(5\times {10}^{-3})\times 50\times 500\times \cos 500t$

$emf=125\cos 500t$

So above is the equation of induced emf

So maximum value of induced emf will be

$em{f}_{max}=125volts$