Question

Two coils each of self-inductance L are connected in parallel. If they are separated by a large distance, then what will be the self-inductance of combination?

• A. $\fracL4$
• B. $\fracL2$
• C. L
• D. 2L

Hint:

Inductors in parallel combine like resistors: $1/Lₑq = 1/L₁ + 1/L₂$.

Answer 1

The Correct Option is B

This question involves determining the equivalent self-inductance of two coils connected in parallel. Each coil has a self-inductance of \(L\). When calculating the equivalent self-inductance for coils in parallel, we use the formula for inductors in parallel.

The formula for the equivalent self-inductance (\(L_{\text{eq}}\)) when two inductors \(L_1\) and \(L_2\) are connected in parallel is:

\(\frac{1}{L_{\text{eq}}} = \frac{1}{L_1} + \frac{1}{L_2}\)

Since both inductors have the same self-inductance, i.e., \(L_1 = L_2 = L\), the formula simplifies to:

\(\frac{1}{L_{\text{eq}}} = \frac{1}{L} + \frac{1}{L} = \frac{2}{L}\)

Solving for \(L_{\text{eq}}\):

\(L_{\text{eq}} = \frac{L}{2}\)

Hence, the self-inductance of the combination of the two coils when connected in parallel is \(\frac{L}{2}\).

Therefore, the correct answer is:

\(\frac{L}{2}\)

Let's confirm this answer by ruling out the other options:

• \(\frac{L}{4}\): Incorrect, as the formula shows \(L_{\text{eq}} = \frac{L}{2}\).
• \(L\): Incorrect, this would be the self-inductance if both were in series, but for parallel, it's less.
• \(2L\): Incorrect, since this represents the inductance if they were in series.