$A$ wire in the form of a tightly wound solenoid is connected to a $DC$ source and carries a current. If the coil is stretched so that there are gaps between successive elements of the spiral coil,will the current increase or decrease? Explain.

(A) When the solenoid is tightly wound,the magnetic field lines are confined within the solenoid,resulting in a high self-inductance $(L)$.
When the coil is stretched,the gaps between the turns increase,which causes the magnetic flux linkage per turn to decrease,leading to a decrease in the self-inductance $(L)$ of the solenoid.
According to the relation $V = L(di/dt) + iR$,for a fixed $DC$ voltage source,the steady-state current is determined by $I = V/R$.
However,during the stretching process,the change in self-inductance induces an electromotive force (emf) $\varepsilon = -L(di/dt) - i(dL/dt)$.
Since the self-inductance $L$ decreases $(dL/dt < 0)$,the induced emf opposes the change,effectively reducing the back-emf. Consequently,the current in the circuit increases.