Two coils $P$ and $S$ have a mutual inductance of $3 \times 10^{-3} \ H$. If the current in the coil $P$ is $I = 20 \sin(50 \pi t) \ A$,then the maximum value of the e.m.f. induced in coil $S$ is (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 $, V$)?

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

An electric current $i_1$ can flow in either direction through loop $(1)$ and induces a current $i_2$ in loop $(2)$. Positive $i_1$ is defined when the current flows from $'a'$ to $'b'$ in loop $(1)$,and positive $i_2$ is defined when the current flows from $'c'$ to $'d'$ in loop $(2)$. In an experiment,the graph of $i_2$ against time $'t'$ is as shown below. Which one$(s)$ of the following graphs could have caused $i_2$ to behave as given above?

Two concentric circular coils having radii $r_1$ and $r_2$ $(r_2 \ll r_1)$ are placed co-axially with centres coinciding. The mutual inductance of the arrangement is ($\mu_0 =$ permeability of free space) (Both coils have single turn).

Two circular coils of radii $r_1$ and $r_2$ $(r_1 \ll r_2)$ are placed coaxially with their centers coinciding. The mutual inductance of the arrangement is