Two coils have mutual inductance $0.002 \ \mathrm{H}$. The current changes in the first coil according to the relation $\mathrm{i}=\mathrm{i}_0 \sin \omega \mathrm{t}$, where $\mathrm{i}_0=5 \mathrm{~A}$ and $\omega=50 \pi$ $\mathrm{rad} / \mathrm{s}$. The maximum value of $\mathrm{emf}$ in the second coil is $\frac{\pi}{\alpha} \mathrm{V}$. The value of $\alpha$ is_______.

The area of its cross-section is $1.2 \times {10^{ - 3}}{m^2}$. Around its central section, a coil of $300$ turns is wound. If an initial current of $2A$ in the solenoid is reversed in $0.25\, sec$, then the $e.m.f$. induced in the coil is

Mutual inductance of two coils can be increased by

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

Two coils $X$ and $Y$ are placed in a circuit such that when a current changes $2A$ in coil $X,$ the magnetic flux changes by $0.4\,weber$ in $Y$. The value of mutual inductance of the coils....$H$

Two circuits have 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 $0.02$ $s$......$V$