Search any question & find its solution
Question:
Answered & Verified by Expert
Two coils have mutual inductance $0.005 \mathrm{H}$. The current changes in the first coil according to equation $I=I_0 \sin \omega t$, where $I_0=10 \mathrm{~A}$ and $\omega=100 \pi \mathrm{rad} \mathrm{s}$. The maximum value of induced emf in the second coil is
Options:
Solution:
2753 Upvotes
Verified Answer
The correct answer is:
$5 \pi$
Mutual inductance, $M=0.005 \mathrm{H}$
$$
\begin{aligned}
& l=I_0 \sin \omega t \\
& I_0=10 \mathrm{~A} \\
& \omega=100 \pi \mathrm{rad} / \mathrm{s}
\end{aligned}
$$
The emf induced in second coil,
$$
e=M \frac{d l}{d t}=M \frac{d l}{d t}=0.005 \times \frac{d l_0 \sin \omega t}{d t}
$$
$\begin{aligned} & =0.005 \times l_0 \omega \cos \omega t=0.005 \times l_0 \omega \cos \frac{2 \pi}{t} t \\ \Rightarrow e_{\max } & =0.005 \times 10 \times 100 \pi \times 1=5 \pi \mathrm{volt}\end{aligned}$
$$
\begin{aligned}
& l=I_0 \sin \omega t \\
& I_0=10 \mathrm{~A} \\
& \omega=100 \pi \mathrm{rad} / \mathrm{s}
\end{aligned}
$$
The emf induced in second coil,
$$
e=M \frac{d l}{d t}=M \frac{d l}{d t}=0.005 \times \frac{d l_0 \sin \omega t}{d t}
$$
$\begin{aligned} & =0.005 \times l_0 \omega \cos \omega t=0.005 \times l_0 \omega \cos \frac{2 \pi}{t} t \\ \Rightarrow e_{\max } & =0.005 \times 10 \times 100 \pi \times 1=5 \pi \mathrm{volt}\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.