Question:
Two identical coils of inductance L joined in series are placed very close to each other such that the winding direction of one coil is exactly opposite to that of the other. The net inductance is
Two identical coils of inductance L joined in series are placed very close to each other such that the winding direction of one coil is exactly opposite to that of the other. The net inductance is
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This principle is used in "non-inductive" resistors where the wire is doubled back on itself to cancel induction.
Updated On: Apr 30, 2026
- $\frac{L}{2}$
- 2 L
- zero
- L
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The Correct Option is C
Solution and Explanation
Step 1: Inductance in Series
For two coils in series with mutual inductance $M$, $L_{net} = L_1 + L_2 \pm 2M$.
Step 2: Opposite Winding
Since they are identical and placed "very close" with opposite winding, the magnetic fields cancel out. This is "opposing" connection, so $L_{net} = L + L - 2M$.
Step 3: Maximum Coupling
For coils very close and identical, $M \approx \sqrt{L \cdot L} = L$.
$L_{net} = 2L - 2L = 0$.
Step 4: Conclusion
The net inductance is zero.
Final Answer:(C)
For two coils in series with mutual inductance $M$, $L_{net} = L_1 + L_2 \pm 2M$.
Step 2: Opposite Winding
Since they are identical and placed "very close" with opposite winding, the magnetic fields cancel out. This is "opposing" connection, so $L_{net} = L + L - 2M$.
Step 3: Maximum Coupling
For coils very close and identical, $M \approx \sqrt{L \cdot L} = L$.
$L_{net} = 2L - 2L = 0$.
Step 4: Conclusion
The net inductance is zero.
Final Answer:(C)
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