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?

$A$ hollow cylinder has length $l$,radius $r$,and thickness $d$,where $l >> r >> d$,and is made of a material with resistivity $\rho$. $A$ time-varying current $I$ flows through the cylinder in the tangential direction. Assume the current is always uniformly distributed along the length of the cylinder. The cylinder is fixed so that it cannot move; assume that there are no externally generated magnetic fields during the time considered for the problems below. Assume current at $t = 0$ to be $I_0$. What is the current $I(t)$ for $t > 0$?

In a coil,the current changes from $-2 \,A$ to $+2 \,A$ in $0.2 \,s$ and induces an emf of $0.1 \,V$. The self-inductance of the coil is: (in $\,mH$)

When a current of $1 \,A$ is passed through a coil of $100$ turns, the flux associated with it is $2.5 \times 10^{-5} \,Wb/\text{turn}$. The self-inductance of the coil in millihenry is:

$A$ coil has $N$ turns and the current passing through it is $I$ ampere, resulting in a self-inductance of $L$ Henry. If the current is doubled, the new self-inductance will be . . . . . . $H$.

$A$ coil and a bulb are connected in series with a $12 \,V$ direct current $(DC)$ source. $A$ soft iron core is now inserted into the coil. Then,