Question

Two coils have a mutual inductance $5mH$. The current changes in the first coil according to equation $I=I_0\sin \omega t$, where, $I_0=10A$ and $\omega =100\pi rad/sec$. The maximum value of emf in the second coil is

• A. $2\pi$
• B. $5\pi$
• C. $\pi$
• D. $4\pi$

Answer 1

The correct option is B

$5\pi$

Step 1: Given data

Mutual inductance, $M=5mH=0.005H$

Current, $I=I_0\sin \omega t$

where, $I_0=10A$

and $\omega =100\pi rad/sec.$

Step 2: Formula used

Emf in the coil,

$\left|\epsilon \right|=M\frac{dI}{dt}$

where $M$ is mutual inductance and $\frac{dI}{dt}$ is the rate of change of current

Step 3: Maximum value of emf in the second coil.

Emf in the coil,

$\left|\epsilon \right|=M\frac{d}{dt}\left(I_0\sin \omega t\right)=M{I}_0\omega \cos \omega t$

Maximum emf,

$\because {\epsilon }_{max}=0.005\times 10\times 100\pi \times 1=5\pi$

The maximum value of emf in the second coil is $5\pi$.

Hence, option B is the correct answer.