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(C) The inductance $L$ of a coil is proportional to the square of the number of turns $N$ and inversely proportional to the length $l$ of the coil. Wh

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$L/4$

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(C) The inductance $L$ of a coil is proportional to the square of the number of turns $N$ and inversely proportional to the length $l$ of the coil. When a coil is cut into two equal parts,the number of turns in each part becomes $N/2$ and the length becomes $l/2$.Since $L \propto N^2/l$,the new inductance $L'$ for each part is $L' = \frac{(N/2)^2}{l/2} = \frac{N^2/4}{l/2} = \frac{1}{2} \frac{N^2}{l} = L/2$.When two inductors $L_1$ and $L_2$ are connected in parallel,the equivalent inductance $L_{eq}$ is given by $\frac{1}{L_{eq}} = \frac{1}{L_1} + \frac{1}{L_2}$.Here,$L_1 = L_2 = L/2$.Therefore,$\frac{1}{L_{eq}} = \frac{1}{L/2} + \frac{1}{L/2} = \frac{2}{L} + \frac{2}{L} = \frac{4}{L}$.Thus,$L_{eq} = L/4$.

An inductor coil of inductance $L$ is cut into two equal parts and both the parts are connected in parallel. The net inductance is

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