In the given circuit,what happens when the switch $S$ is opened?

In a circular coil,when the number of turns is doubled and the resistance becomes $1/4$th of the initial value,then the inductance becomes ....... times.

An air-cored solenoid with length $20 \, cm$,area of cross-section $20 \, cm^2$,and number of turns $400$ carries a current of $2 \, A$. The current is suddenly switched off within $10^{-3} \, s$. The average back $emf$ induced across the ends of the open switch in the circuit is (ignore the variation in magnetic field near the ends of the solenoid) ........ $V$.

The following figure represents two bulbs $B_1$ and $B_2$, a resistor $R$, and an inductor $L$. When the switch $S$ is turned off, which of the following statements is true?

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:

Define the unit of self-inductance. On which factors does self-inductance depend?