$A$ current $I = 10 \sin(100 \pi t) \text{ A}$ is passed in a coil, which induces a maximum emf of $5 \pi \text{ V}$ in a neighboring coil. The mutual inductance of the two coils is: (in $\text{ mH}$)

$A$ solenoid of length $0.30 \, m$ has $2000$ turns. The area of its cross-section is $1.2 \times 10^{-3} \, m^2$. Around its central section,a coil of $300$ turns is wound. If an initial current of $2 \, A$ in the solenoid is reversed in $0.25 \, s$,then the $e.m.f.$ induced in the coil is:

The mutual inductance of two coils is $8 \ mH$. The current in one coil changes according to the equation $I = 12 \sin 100t$,where $I$ is in ampere and $t$ is time in second. The maximum value of emf induced in the second coil is (in $V$)

The induction coil works on the principle of

If a change in current of $0.01\, A$ in one coil produces a change in magnetic flux of $1.2 \times 10^{-2}\,Wb$ in the other coil,then the mutual inductance of the two coils in henries is.....$H$

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.....$V$.