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

The number of turns of primary and secondary coils of a transformer are $5$ and $10$ respectively and the mutual inductance of the transformer is $25\,H$. Now,the number of turns in the primary and secondary of the transformer are made $10$ and $5$ respectively. The mutual inductance of the transformer in henry will be:

Two coils $A$ and $B$ having turns $300$ and $600$ respectively are placed near each other. On passing a current of $3.0 \ A$ in coil $A$, the magnetic flux linked with coil $A$ is $1.2 \times 10^{-4} \ Wb$ and with coil $B$ it is $9.0 \times 10^{-5} \ Wb$. The mutual inductance of the system is:

An alternating current of peak value $\left(\frac{2}{\pi}\right) \text{ A}$ flows through the primary coil of a transformer. The coefficient of mutual inductance between the primary and secondary coils is $1 \text{ H}$. What is the peak electromotive force (e.m.f.) induced in the secondary coil (in $\text{ V}$)? (Frequency of a.c. $= 50 \text{ Hz}$)

What is the coefficient of mutual inductance when the magnetic flux changes by $2 \times 10^{-2} \, Wb$ and the change in current is $0.01 \, A$?

$A$ coil of radius $1\, cm$ and $100$ turns is placed in the middle of a long solenoid of radius $5\, cm$ having $5\, turns/cm$, with its axis parallel to the axis of the solenoid. The mutual inductance in millihenry is: