Two coils have a mutual inductance of $0.004 \ H$. The current changes in the first coil according to the equation $I = I_0 \sin \omega t$,where $I_0 = 10 \ A$ and $\omega = 50 \pi \ rad \ s^{-1}$. The maximum value of e.m.f. in the second coil in volt is (in $\pi$)

An alternating current of angular frequency $\omega = 200 \, rad/sec$ and peak value $I_0 = 1 \, A$,as shown in the figure,is applied to the primary coil of a transformer. If the coefficient of mutual induction between the primary and the secondary coil is $M = 1.5 \, H$,the magnitude of the induced voltage in the secondary coil will be.....$V$.

Two coils $A$ and $B$ are placed in a circuit. When current in the coil $A$ changes by $0.8 \,A$, the magnetic flux in coil $B$ changes by $0.16 \,Wb$. The mutual inductance between the coils is (in $\,H$)

If a change in current of $0.01 \,A$ in one coil produces a change in magnetic flux of $2 \times 10^{-2} \,Wb$ in the other coil,then the mutual inductance of the two coils in henry is (in $\,H$)

$A$ pair of adjacent coils has a mutual inductance of $1.5\; H$. If the current in one coil changes from $0$ to $20\; A$ in $0.5\; s$,what is the change of flux (in $Wb$) linkage with the other coil?

If a current of $3.0 \ A$ flowing in the primary coil is reduced to zero in $0.001 \ s$,then the induced $e.m.f.$ in the secondary coil is $15000 \ V$. The mutual inductance between the two coils is (in $H$):