Question

Two coils have a mutual inductance of $0.01H$. The current changes in the first coil according to the equation, $I=5\sin \left(200\pi t\right)$. What is the maximum value of emf induced in the second coil?

• A. $\pi V$
• B. $10\pi V$
• C. $0.1\pi V$
• D. $0.01\pi V$

Answer 1

The correct option is B

$10\pi V$

Step 1: Given that

Two coils having mutual inductance i.e. $M=0.01H$

The alternating current is given by, $I=5\sin \left(200\pi t\right)$

Step 2: Formula used

Now the value of emf ($\epsilon$) in the secondary coil can be given by,

$\epsilon =M\frac{dI}{dt}$

Step 3: Find the value of emf induced in the secondary coil.

So,

$\begin{array}{rcl}\epsilon & =& M\frac{d}{dt}\left(5\sin \left(200\pi t\right)\right)\\ & =& 0.01\times 5\cos \left(200\pi t\right)\times 200\pi \\ & =& 10\pi \cos \left(200\pi t\right)........\left(1\right)\end{array}$

Step 4: Calculate the maximum value of emf induced in the secondary coil.

For the maximum value of emf, $\cos \left(200\pi t\right)=1$, now putting this value equation (1), can be written as,

${\epsilon }_{max}=10\pi V$

Thus, the maximum value of emf induced in the second coil is$10\pi V$.

Hence, the correct answer is option (B).