$X$ and $Y$ are two circuits having a coefficient of mutual inductance $3 \text{ mH}$ and resistances $10 \text{ } \Omega$ and $4 \text{ } \Omega$ respectively. To have an induced current of $60 \times 10^{-4} \text{ A}$ in circuit $Y$,the amount of current to be changed in circuit $X$ in $0.02 \text{ s}$ is: (in $A$)

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 . . . . . . $A/s$.

An alternating current with an angular frequency of $\omega = 200\,rad/s$ and a peak value of $I_0 = 1\,A$,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 coils is $M = 1.5\,H$,the magnitude of the induced voltage in the secondary coil will be.....$V$.

$A$ small square loop of wire of side $l$ is placed inside a large square loop of side $L$ $(L > l)$. If the loops are coplanar and their centers coincide,the mutual inductance of the system is directly proportional to

Give two definitions of mutual inductance, give its units and write factors on which its value depends.

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: