A square shaped coil of area $70 {\mathrm{cm}}^2$ having $600$ turns rotates in a magnetic field of $0.4 \mathrm{Wb} {\mathrm{m}}^{–2}$, about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If the coil completes $500$ revolution in a minute, the instantaneous emf when the plane of the coil is inclined at $60°$ with the field, will be ______ $\mathrm{V}$.

(Take $\pi \mathit{=}\frac{\mathit{22}}{\mathit{7}}$)

In the given circuit the $\mathrm{AC}$ source has $\omega =100 \mathrm{rad} {\mathrm{s}}^{-1}$. Considering the inductor and capacitor to be ideal, what will be the current $I$ flowing through the circuit?

A bar magnet is passing through a conducting loop of radius $R$ with velocity $v.$ The radius of the bar magnet is such that it just passes through the loop. The induced e.m.f. in the loop can be represented by the approximate curve:

The alternating current is given by, $i=\left\{\sqrt{42}\sin \left(\frac{2\pi }{T}t\right)+10\right\} \mathrm{A}$. The R.M.S. value of this current is __________ $\mathrm{A}$.

A constant magnetic field of $1 \mathrm{T}$ is applied in the $\mathrm{x}>0$ region. A metallic circular ring of radius $1 \mathrm{m}$ is moving with a constant velocity of $1 \mathrm{m} {\mathrm{s}}^{-1}$ along the $x$-axis. At $t=0 \mathrm{s}$, the centre $\mathrm{O}$ of the ring is at $\mathrm{x}=-1 \mathrm{m}$. What will be the value of the induced emf in the ring at $\mathrm{t}=1 \mathrm{s}$ ? (Assume the velocity of the ring does not change.)