$A$ pair of adjacent coils have a mutual inductance, $M$. The current in one coil changes from $0 \,A$ to $16 \,A$ in $0.3 \,s$, and the change of flux linkage with the other coil is $40 \,Wb$. The value of $M$ is: (in $\,H$)

$A$ long straight wire is placed along the axis of a circular ring of radius $R$. The mutual inductance of this system is

$A$ 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 circular coils have their centers at the same point. The mutual inductance between them will be maximum when their axes

Two coaxial coils $A$ and $B$ of radii $R_{1}$ and $R_{2}$ are placed in the same plane $(R_{2} > R_{1})$. If a current is passed through coil $B$,the coefficient of mutual inductance between the coils is proportional to:

Two coaxial coils are very close to each other and their mutual inductance is $5 \,mH$. If a current $i = 50 \sin(500t) \,A$ is passed in one of the coils,then the peak value of the induced e.m.f. in the secondary coil will be ........... $V$.