A coil of inductance \(L\) is divided into four equal parts and all the parts are connected in parallel. The…
A coil of inductance \(L\) is divided into four equal parts and all the parts are connected in parallel. The effective inductance of the combination is
\(\frac{L}{4}\)
\(\frac{L}{8}\)
\(\frac{L}{16}\)
\(4 L\)
Solution
Since, coil of inductance \(L\) is divided into four equal parts.
Hence, inductance of each part is same and equal to \(\frac{L}{4}\).
i.e., \(\quad L_1=L_2=L_3=L_4=\frac{L}{4}\)
Since, \(L_1, L_2, L_3\) and \(L_4\) are connected in parallel. Hence, effective inductance \(L^{\prime}\) of the combination is given as
\(\begin{aligned}
\frac{1}{L^{\prime}} & =\frac{1}{L_1}+\frac{1}{L_2}+\frac{1}{L_3}+\frac{1}{L_4} \\
& =\frac{1}{L / 4}+\frac{1}{L / 4}+\frac{1}{L / 4}+\frac{1}{L / 4} \\
& =\frac{4}{L}+\frac{4}{L}+\frac{4}{L}+\frac{4}{L} \\
\Rightarrow \frac{1}{L^{\prime}} & =\frac{16}{L} \Rightarrow L^{\prime}=\frac{L}{16}
\end{aligned}\)