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 (Both coils have single turn, $\mu_0$ = permeability of free space)

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?

The device that does not work on the principle of mutual induction is

Two circular coils can be arranged in any of the three situations shown in the figure. Their mutual inductance will be

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

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