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.)

For the given circuit the current $i$ through the battery when the key in closed and the steady state has been reached is