Question

Three coils of inductance, \(L_1\) = 2 H, \(L_2\) = 3 H and \(L_3\) = 6 H are connected so that they are separated from each other. To obtain the effective inductance of \(\frac{18}{11}\) H between points A and B, out of the following figures, the correct one is

• A. \(P\)
• B. \(S\)
• C. \(Q\)
• D. \(R\)

Hint:

Evaluate the effective inductance of each arrangement (coils are far apart, so no mutual inductance).

Answer 1

The Correct Option is B

Step 1: Look for a 9 H branch
$\frac{18}{11}=\frac{2\times9}{2+9}$, so we need 2 H in parallel with 9 H, where $9=3+6$.

Step 2: Match the figure
Only (S) has $L_1$ alone on one path and $L_2$ with $L_3$ in series on the other path. So (S), option (B).

Final Answer:
Figure (S) gives 18/11 H, option (B). \[ \boxed{S} \]