The current flowing in a coil of self-inductance $0.4 \, mH$ is increased by $250 \, mA$ in $0.1 \, s$. The induced $e.m.f.$ will be:

Regarding self-inductance:
$A:$ The self-inductance of the coil depends on its geometry.
$B:$ Self-inductance does not depend on the permeability of the medium.
$C:$ Self-induced e.m.f. opposes any change in the current in a circuit.
$D:$ Self-inductance is the electromagnetic analogue of mass in mechanics.
$E:$ Work needs to be done against self-induced e.m.f. in establishing the current.
Choose the correct answer from the options given below:

Two different coils have self-inductance $3L$ and $L$. The current in both the coils is increased at the same constant rate. At a certain instant of time, the power given to the two coils is same. At that time, there was current and voltage induced in the two coils. At the same instant, the ratio of energy stored in the first coil to that in the second coil is

Two coils have self-inductance $L_1$ and $L_2$. The current through them is increasing at a constant rate. If the power dissipated in both the coils is the same, then the ratio of energy stored in the coil having inductance $L_1$ to that in $L_2$ is

Current in a coil changes from $4 \,A$ to zero in $0.1 \,s$ and the emf induced is $100 \,V$. The self inductance of the coil is (in $\,H$)

Explain self-induction and obtain the equation for the self-induced $emf$ in a coil.