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Alexphysics edited Jun 25, 2026, 1:15 PM

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		+	### Statement
		+
		+	$11.3.14.$ [Insert the problem statement]
		+
		+	### Solution
		+
		+	For two ideal inductors with self‑inductances$ L_1 $and $L_2$ and mutual inductance coefficient $M = L_{12}$, connected in series
		+
		+	the total magnetic flux may be reinforced or partially cancelled depending on the relative orientation of the windings. The total inductance of the circuit is:
		+
		+	$\boxed{L_{\text{total}} = L_1 + L_2 \pm 2L_{12}}$
		+
		+	The positive sign is taken when the currents in both coils produce magnetic fields that add (series‑aiding connection, fluxes in the same direction); the negative sign corresponds to fields that oppose each other (series‑opposing connection, fluxes in opposite directions).
		+
		+
		+	#### Answer
		+
		+	[Insert a concise answer or boxed result]

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			### Statement

			$11.3.14.$ [Insert the problem statement]

			### Solution

			For two ideal inductors with self‑inductances$ L_1 $and $L_2$ and mutual inductance coefficient $M = L_{12}$, connected in series

			the total magnetic flux may be reinforced or partially cancelled depending on the relative orientation of the windings. The total inductance of the circuit is:

			$\boxed{L_{\text{total}} = L_1 + L_2 \pm 2L_{12}}$

			The positive sign is taken when the currents in both coils produce magnetic fields that add (series‑aiding connection, fluxes in the same direction); the negative sign corresponds to fields that oppose each other (series‑opposing connection, fluxes in opposite directions).


			#### Answer

			[Insert a concise answer or boxed result]