What length of a very thin wire is required to obtain a solenoid of length $l_0$ and inductance $L$?

The self-inductance $L$ of a solenoid of length $l$ and area of cross-section $A$ increases . . . . . . (Here with a fixed number of turns $N$).

$A$ solenoid is connected to a battery so that a steady current flows through it. If an iron core is inserted into the solenoid, will the current increase or decrease? Explain.

$A$ circuit having a self-inductance of $1 \text{ H}$ carries a current of $1 \text{ A}$. To prevent sparking when the circuit is broken,a capacitor which can withstand $500 \text{ V}$ is connected across the switch. What is the minimum value of the capacitance of the capacitor (in $\mu \text{ F}$)?

The self-inductance of a coil is $50 mH$. When a current of $1 A$ passing through the coil reduces to zero at a steady rate in $0.1 s$,find the self-induced emf. (in $V$)

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