Question

The equivalent inductance between A and B is equal to

• A. \(\frac{4}{5}\mathrm{H}\)
• B. \(\frac{5}{4}\mathrm{H}\)
• C. \(\frac{3}{10}\mathrm{H}\)
• D. 15 H

Hint:

Trace the wires: all four inductors turn out to be connected directly between the same two points, so they are in parallel.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
Identify the nodes. The wire from A goes over the top to the right end of the 4 H coil and the top of the 3 H coil. The junction after the 2 H coil is joined by the lower wire to B.

Step 2: Connections
2 H: between A and B. 3 H: between A and B. 4 H: between B and A. 6 H: between A and B.
So all four inductors are in parallel (no mutual inductance).

Step 3: Calculation
\(\dfrac{1}{L}=\dfrac12+\dfrac13+\dfrac14+\dfrac16=\dfrac{6+4+3+2}{12}=\dfrac{15}{12}\).

Step 4: Result
\(L=\dfrac{12}{15}=\dfrac45\ \text{H}\), option (A).

Final Answer:
The equivalent inductance is 4/5 H. \[ \boxed{\text{(A) }\dfrac{4}{5}\,\text{H}} \]