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
Show Hint
Evaluate the effective inductance of each arrangement (coils are far apart, so no mutual inductance).
Step 1: Understanding the Concept
Inductors follow the same rules as resistors when there is no mutual coupling: series adds, parallel adds reciprocals. \(L_1=2\) H, \(L_2=3\) H, \(L_3=6\) H.
Step 2: Key Formula or Approach
Read each figure carefully and compute its effective value.
Step 3: Detailed Explanation
(P) All three in series: \(2+3+6=11\) H.
(Q) All three in parallel: \(\dfrac1L=\dfrac12+\dfrac13+\dfrac16=1\), so \(L=1\) H.
(R) \(L_1\) and \(L_2\) in series (5 H) joined across \(L_3\) in parallel: \(\dfrac{5\times6}{11}=\dfrac{30}{11}\) H.
(S) \(L_1\) is directly between A... In this figure, \(L_1\) connects the two terminals A and B on one path, while \(L_2\) and \(L_3\) in series (9 H) form the other path. So \(L_1\parallel(L_2+L_3)\): \(\dfrac{2\times9}{2+9}=\dfrac{18}{11}\) H.
Final Answer:
Figure (S) gives \(\frac{18}{11}\) H, option (B).
\[ \boxed{S\ \text{(B)}} \]
