Правка разделов «Statement», «Answer»
en/11.3.14.md
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| @@ -1,6 +1,8 @@ | |||
| ### Statement | |||
| − | $11.3.14.$ | ||
| + | $11.3.14.$ | ||
| + | The circuit consists of two series-connected inductors L1and L2. Mutual in- | ||
| + | ductance of the L12coils. Find the total inductance of the circuit. | ||
| ### 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). | |||
| @@ -15,4 +17,4 @@Solution | |||
| #### Answer | |||
| − | [Insert a concise answer or boxed result] | ||
| + | $\boxed{L_{\text{total}} = L_1 + L_2 \pm 2L_{12}}$ | ||
| @@ -1,6 +1,8 @@ | |||
| ### Statement | ### Statement | ||
| $11.3.14.$ |
$11.3.14.$ | ||
| The circuit consists of two series-connected inductors L1and L2. Mutual in- | |||
| ductance of the L12coils. Find the total inductance of the circuit. | |||
| ### Solution | ### Solution | ||
| For two ideal inductors with self‑inductances$ L_1 $and $L_2$ and mutual inductance coefficient $M = L_{12}$, connected in series | 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: | 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: | ||
| $\boxed{L_{\text{total}} = L_1 + L_2 \pm 2L_{12}}$ | $\boxed{L_{\text{total}} = L_1 + L_2 \pm 2L_{12}}$ | ||
| 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). | 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). | ||
| @@ -15,4 +17,4 @@Solution | |||
| #### Answer | #### Answer | ||
| [Insert a concise answer or boxed result] | $\boxed{L_{\text{total}} = L_1 + L_2 \pm 2L_{12}}$ | ||