An $e.m.f.$ of $100$ $mV$ is induced in a coil when the current in another nearby coil changes from $0$ to $10$ $A$ in $0.1$ $s$. The coefficient of mutual induction between the two coils is $...$ $mH$.

Two coils have a mutual inductance of $0.005 \ H$. The current changes in the first coil according to the equation $I = I_0 \sin \omega t$,where $I_0 = 10 \ A$ and $\omega = 100 \pi \ rad/s$. The maximum value of the induced emf in the second coil is:

$A$ long straight wire carrying current $I$ and a rectangular frame with side lengths $a$ and $b$ lie in the same plane as shown in the figure. The mutual inductance of the wire and frame is

Two coils of self-inductances $2\, mH$ and $8\, mH$ are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is......$mH$.

The mutual inductance between the rectangular loop and the long straight wire as shown in the figure is $M$.

The mutual inductance between two coils is $1.25 \ H$. If the current in the primary coil changes at the rate of $80 \ A/s$, then the induced $e.m.f.$ in the secondary coil is ...... $V$.