The mutual inductance of an induction coil is $5\,H$. In the primary coil,the current reduces from $5\,A$ to zero in $10^{-3}\,s$. What is the induced emf in the secondary coil in $V$?

Two circuits have a mutual inductance of $0.1\, H$. What average $e.m.f.$ is induced in one circuit when the current in the other circuit changes from $0$ to $20\, A$ in $0.02\, s$ (in $, V$)?

$A$ coil of radius $r$ is placed on another coil (whose radius is $R$ and current flowing through it is changing) so that their centres coincide. $(R \gg r)$ If both the coils are coplanar,then the mutual inductance between them is proportional to

$A$ long solenoid '$S$' has 'n' turns per meter,with diameter 'a'. At the centre of this coil we place a smaller coil of '$N$' turns and diameter 'b' (where $b < a$). If the current in the solenoid increases linearly with time,what is the induced emf appearing in the smaller coil? Plot a graph showing the nature of variation in emf,if current varies as a function of $I(t) = mt^2 + C$.

Two coils have a mutual inductance of $0.004 \ H$. The current changes in the first coil according to the equation $I = I_0 \sin \omega t$,where $I_0 = 10 \ A$ and $\omega = 50 \pi \ rad \ s^{-1}$. The maximum value of e.m.f. in the second coil in volt is (in $\pi$)

Consider a conducting wire of length $L$ bent in the form of a circle of radius $R$ and another conductor of length $a$ $(a \ll R)$ is bent in the form of a square. The two loops are then placed in the same plane such that the square loop is exactly at the centre of the circular loop. What will be the mutual inductance between the two loops?