Two coils having self-inductance $L_1 = 75 \text{ mH}$ and $L_2 = 48 \text{ mH}$ are coupled with each other. If the mutual inductance of the coils is $37.2 \text{ mH}$, then the coefficient of coupling will be:

When a current of $4 \,A$ changes to $8 \,A$ in $0.6 \,s$ in a primary coil, it induces an e.m.f. of $50 \,mV$ in the secondary coil. The mutual inductance between the two coils is: (in $\,mH$)

$A$ transformer works on the principle of

$A$ 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 coils of self-inductance $25 \ mH$ and $9 \ mH$ are placed close together such that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is (in $mH$)

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: