The mutual inductance between a primary and secondary circuit is $0.5 \, H$. The resistances of the primary and the secondary circuits are $20 \, \Omega$ and $5 \, \Omega$ respectively. To generate a current of $0.4 \, A$ in the secondary,the current in the primary must be changed at the rate of . . . . . . $A/s$.

In a transformer, the coefficient of mutual inductance between the primary and the secondary coil is $0.2 \, H$. When the current changes by $5 \, A/s$ in the primary, the induced $e.m.f.$ in the secondary will be......$V$

The inductors of two $LR$ circuits are placed next to each other,as shown in the figure. The values of the self-inductance of the inductors,resistances,mutual-inductance,and applied voltages are specified in the given circuit. After both the switches are closed simultaneously,the total work done by the batteries against the induced $EMF$ in the inductors by the time the currents reach their steady-state values is . . . . $mJ$.

$A$ 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?

$A$ long straight wire is placed along the axis of a circular ring of radius $R$. The mutual inductance of this system is

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 $...$ $mH$.