The induction coil works on the principle of

Two coils,$X$ and $Y$,are kept in close vicinity of each other. When a varying current,$I(t)$,flows through coil $X$,the induced emf $(V(t))$ in coil $Y$ varies in the manner shown in the figure. The variation of $I(t)$ with time can then be represented by the graph labeled as:

Two concentric circular coils having radii $r_{1}$ and $r_{2}$ $(r_{2} \ll r_{1})$ are placed coaxially with centers coinciding. The mutual inductance of the arrangement is (Both coils have a single turn) ($\mu_{0} =$ permeability of free space).

The coefficient of mutual inductance between the primary and the secondary coil of a transformer is $0.2 H$. When the current in the primary coil changes at a rate of $5 A s^{-1}$,the induced emf in the secondary coil will be: (in $V$)

Two coils have a mutual inductance of $0.005 \ H$. The current changes in the first coil according to the equation $I = I_0 \sin \omega t$,where $I_0 = 10 \ A$ and $\omega = 100 \pi \ rad/s$. The maximum value of the induced emf in the second coil 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. $= 50 \text{ Hz}$)