Two coils $P$ and $S$ have a mutual inductance of $3 \times 10^{-3} \ H$. If the current in the coil $P$ is $I = 20 \sin(50 \pi t) \ A$,then the maximum value of the e.m.f. induced in coil $S$ is (in $V$)

Two concentric circular coils,one of small radius $r$ and the other of large radius $R$,are placed coaxially with their centers coinciding. If the radius $r$ is changed by $2 \%$,then the change in mutual inductance of the arrangement is (assume $r \ll R$). (in $\%$)

Two circular coils have their centers at the same point. The mutual inductance between them will be maximum when their axes

$A$ primary coil and a secondary coil are placed close to each other. $A$ current, which changes at the rate of $25 \, A$ in a millisecond, is present in the primary coil. If the mutual inductance is $92 \times 10^{-6} \, H$, then the value of the induced emf in the secondary coil is:

$X$ and $Y$ are two circuits having a coefficient of mutual inductance $3 \text{ mH}$ and resistances $10 \text{ } \Omega$ and $4 \text{ } \Omega$ respectively. To have an induced current of $60 \times 10^{-4} \text{ A}$ in circuit $Y$,the amount of current to be changed in circuit $X$ in $0.02 \text{ s}$ is: (in $A$)

Two coils have a mutual inductance of $ 0.005 \ H $. The current changes in the first coil according to the equation $ i = i_{m} \sin \omega t $,where $ i_{m} = 10 \ A $ and $ \omega = 100 \pi \ rad \ s^{-1} $. The maximum value of the emf induced in the second coil is: