What does this black point mean?i mean because what reason ,so we will say the inductance of the circuit below can be written as this,by the way , \$M\$ means Mutual inductance.

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Also,i want to ask that Why can the inductance of the circuit below be calculated like this? enter image description here

\$L_{AB}=L_1+L_2+L_3+2M_{12}-2M_{13}-2M_{23}=3+7+10+(2\times2)-(2\times1)-(2\times 3)=16H\$

  • \$\begingroup\$ The black point means, the "polarity" of the coils in relation to each other. \$\endgroup\$ – vtolentino Apr 30 '20 at 13:26
  • \$\begingroup\$ do you understand what mutual inductance means? The dots simply represent the polarity of the influence the inductors have on each other \$\endgroup\$ – FrancoVS Apr 30 '20 at 14:05
  • \$\begingroup\$ @shineele do you understand what mutual inductance is about? \$\endgroup\$ – Andy aka Apr 30 '20 at 14:30
  • \$\begingroup\$ @Andyaka Not totally understand about mutual inductance \$\endgroup\$ – shineele Apr 30 '20 at 14:56
  • \$\begingroup\$ OK, wasn't sure from the way you phrased the question. \$\endgroup\$ – Andy aka Apr 30 '20 at 14:58

The dots indicate the direction of the magnetic coupling. In your final circuit, L1 and L2 are coupled so their magnetic fields add, increasing the total inductance; L3, coupled oppositely so the magnetic fields of L1 and L2 are in opposition to L3 (thereby canceling the magnetic field to some extent), decreases the total inductance. A similar notation indicates the polarity of a transformer coupling.

  • \$\begingroup\$ Do you have some figure to describe what you say?because you said " L1 and L2 are coupled so their magnetic fields add, increasing the total inductance",it is abstract to me \$\endgroup\$ – shineele Apr 30 '20 at 13:42
  • \$\begingroup\$ I'm talking about the last figure in your post, with three inductors in series. The dots show which direction the magnetic field is in, based on the direction of the current. When the magnetic fields are in the same direction, they add to each other; when they're in opposite directions, they cancel. \$\endgroup\$ – Cristobol Polychronopolis Apr 30 '20 at 13:46
  • \$\begingroup\$ so like the first figure in my post,it means that direction of current of both inductor are from "left to the right"? so their inductance and Mutual inductance. can be added together? \$\endgroup\$ – shineele Apr 30 '20 at 13:54
  • 1
    \$\begingroup\$ That's right. In a series circuit (drawn linearly, as those above) the inductors with the dots on the same side add the inductance due to coupling, and on opposite sides they subtract. That's why, in the second 3-inductor example, the M12 term is added (L1 and L2 couple constructively) but the M13 and M23 are subtracted (L3 is opposite in coupling direction to both L1 and L2). \$\endgroup\$ – Cristobol Polychronopolis Apr 30 '20 at 14:33
  • \$\begingroup\$ @shineele In your drawings the dots do not indicate the direction of the current flow, but instead the direction of the magnetic field produced by the inductors. Think of two magnets in close proximity to each other. Facing one way they push apart, but then flip one around and now they pull together. The dot is about the magnetic field. \$\endgroup\$ – Aaron Apr 30 '20 at 16:00

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