$A$ small coil of radius $r$ is placed at the centre of a large coil of radius $R$,where $R >> r$. The coils are coplanar. The coefficient of mutual inductance between the coils is

The coefficient of mutual inductance of two coils is $6\, mH$. If the current flowing in one is $2\, A$,then the induced $e.m.f.$ in the second coil will be:

Two circuits have a coefficient of mutual induction of $0.09 \ H$. The average $e.m.f.$ induced in the secondary circuit due to a change of current from $0 \ A$ to $20 \ A$ in $0.006 \ s$ in the primary circuit will be:

Two coils have mutual inductance $0.002 \ H$. The current changes in the first coil according to the relation $i = i_0 \sin \omega t$,where $i_0 = 5 \ A$ and $\omega = 50 \pi \ rad/s$. The maximum value of $emf$ in the second coil is $\frac{\pi}{\alpha} \ V$. The value of $\alpha$ is . . . . . . .

The coefficient of mutual induction is $2 \text{ H}$ and the induced e.m.f. across the secondary is $2 \text{ kV}$. The current in the primary is reduced from $6 \text{ A}$ to $3 \text{ A}$. The time required for the change of current is:

$A$ circular loop of radius $0.3 \, cm$ lies parallel to a much bigger circular loop of radius $20 \, cm$. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is $15 \, cm$. If a current of $20 \, A$ flows through the smaller loop,then the flux linked with the bigger loop is: