Consider two coils in which a current in one coil carrying $6$ A causes the change in the flux in the second coil $12 \times 10^{-4}$ weber/turn. The second coil has $2000$ turns. The mutual inductance between the coils is

Magnetic flux linked with the coil in weber is given by the equation $\Phi = 5t^2 + 6t + 11$. The e.m.f. induced in the coil in the $5^{\text{th}}$ second will be

Two coils A and B have 180 and 360 turns respectively. The current of 1A flows through both the coils. Due to current of 1A in coil A, flux per turn of $0.8 \times 10^{-3}$ Wb is linked with coil A. Due to current of 1A in coil B, flux per turn of $1 \times 10^{-3}$ Wb is linked with coil B. The self inductance of coil A is $L_A$ and the self inductance of coil B is $L_B$. The ratio $L_A$ to $L_B$ is

If current of 4 A produces magnetic flux of $3 \times 10^{-3}$ Wb through a coil of 400 turns, the energy stored in the coil will be