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This video illustrates a method for determine the
signs in the coupled coil equations.
In the equations of magnetically coupled coils,
the voltage in each coil does depend
not only on the current flowing through it,
but it also depends on the intensity
flowing through the coil to which is coupled.
Sign of the term containing the autoinductance coefficient L1
We look at the current reference
flowing in coil 1 and the voltage reference
of coil 1. As voltage and current references
have the same sense in the coil (both
from 1 to 1 ') the sign of the term containing L1 is positive.
Sign of the term containing the autoinductance coefficient L2
We look at the reference of the
current flowing through the coil 2 and in the
reference voltage of Coil 2. • Since
voltage and current references are oposite
in the coil 2 (the intensity goes from
terminal 2 to 2 'and the reference voltage goes from 2' to 2)
Thus, the sign of the term that contains L2 is negative.
sign of the term containing the mutual induction coefficient M12:
We look at the reference of the current flowing in the coil 2,
in the voltage reference in coil 1
and in the corresponding terminals of both coils
The current reference in coil 2
enters the terminal marked with the point.
The equivalent intensity flowing through the coil 1 creates
therein the same effect as the current i2 flowing through the coil 2
The equivalent current enters
the terminal marked with the point in coil 1,
(in the same way that i2). • As the voltage reference
in the coil 1 and the equivalent intensity
of coil 2 that flows through the coil 1 are opposite there
(equivalent intensity goes from terminal 1' to 1
and the reference voltage goes from 1 to 1').
Thus, the sign of the term containing M12 is negative.
Sign of the term containing the coefficient of mutual induction M21:
We look at the reference of the current flowing through the coil 1
the reference voltage across the coil 2
and the corresponding terminals of both coils.
The current in the coil 1 outputs
from the terminal marked point.
The equivalent intensity circulating in the coil 2 creates
the same effect as it created in the coil 2 by the current i1
flowing through the coil 1, Both currents output from
the terminals with a point mark.
As the reference voltage on the coil 2 and the equivalent current
flowing through the coil 2 have
the same direction in said coil
(both references are from terminal 2 'to 2),
then the sign of term is M21 is positive.
Finally, the equations of both coils are shown with the signs of the terms
that relate coil voltages with currents flowing through them.
The conclusion of this example is that the signs of the equations
of the coupled coils depend on the references of voltages and currents
as well as the marked terminals.
The procedure used here is general and
it can be applied in cases with
three or more coupled coils.