Question

A uniformly wound solenoidal coil of self-inductance $1.8\times {10}^{-4}$ henry and resistance 6 ohm is broken up into two coils having lengths in the ratio 1 : 2. These identical coils are then connected in parallel across a 12 volt battery of negligible resistance. The steady state current through the battery is___ ampere.

Answer 1

When the coil is broken up into two, each part will have resistance proportional to its length, and there are then joined in parallel.
The given circuit becomes equivalent to that shown in figure.

In steady state inductance becomes ineffective, ie., the combination behaves as a simple conductor
$I_s=\frac{12}{4}+\frac{12}{2}=9A$