Why is the mutual inductance term negative in the loop equations?

In summary, while reviewing old studies, the speaker realizes that they were given a question to find Zeq at the terminals of the left hand inductor using a 1V test. They also mention running their loop current equations for the circuit and being told that the mutual inductance term should be negative in both equations. After some consideration and clarification, the speaker realizes that the loop equation needs to be adjusted for I1 running from - to + potential.
  • #1
xxXen0xx
2
0
http://img638.imageshack.us/img638/989/newbitmapimagety.png
I am running my loop current equations for this circuit and have.
-1+-j6*(I1-I2)=0
-j6*(I2-I1)+j20*I2 +j12*I3=0
(j30-j2+j5+4)*I3+j12*I2=0

But i am being told that the mutual inductance term j12 should be negative in both.
My model current I2 is going into the dot and I3 is coming out of the dot, so
jwL+M=0 should apply
not
jwL-M=0

what am i missing?
o wait... is it the sign of the 1V i have backwards?
 
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  • #2
what is the question?
 
  • #3
I am reviewing questions from old studies.
I believe it was to find Zeq at the terminals of the left hand inductor, by using a 1V test.
But i think I answered my own question.
For I1 running from - to + potential the loop equation needs to read
1+-j6*(I1-I2)=0
so that second loop equation is
-j6*(I2-I1)+j20*I2 +j12*I3=0
 

What is mutual inductance?

Mutual inductance is the phenomenon in which a changing current in one circuit induces a voltage in another nearby circuit.

How does mutual inductance work in a circuit?

In a circuit with mutual inductance, the changing magnetic field created by the current in one coil will pass through the other coil, inducing a voltage in the second coil. This voltage can then drive a current in the second coil.

What is the formula for calculating mutual inductance?

The formula for mutual inductance is M = k * (N1 * N2 * A) / l, where M is the mutual inductance, k is the coupling coefficient, N1 and N2 are the number of turns in the two coils, A is the common area between the coils, and l is the length of the coils.

What is the unit of measurement for mutual inductance?

The unit of measurement for mutual inductance is the Henry (H).

What are some practical applications of mutual inductance circuits?

Mutual inductance circuits are commonly used in transformers, where they are used to step up or step down voltages. They are also used in wireless charging systems and inductance sensors. Additionally, mutual inductance is an important concept in the study of electromagnetics and is used in many electronic devices such as motors, generators, and antennas.

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