# Kirchoff's voltage law with coils

There is an idea that Kirchoff's voltage law could not be applied to circuit containing coils like this link.

What makes me confused is that almost all books apply Kirchoff's voltage law to RL and RLC circuit.

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mfb
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There is an idea that Kirchoff's voltage law could not be applied to circuit containing coils like this link.
You have to modify the formulas to include external changing magnetic fields, here you just have to add 1V for going around the coil once (mainly at 5:55).

What makes me confused is that almost all books apply Kirchoff's voltage law to RL and RLC circuit.
Those circuits do not have external changing magnetic fields in them. Coils as part of a circuit are not an issue as long as the circuit itself (where you do your calculations) is not used as a coil.

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Thanks mfb, your comment are useful.

How can we find the value read by the voltmeter when connected to A and D measuring the voltage Va - Vd?

mfb
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With Kirchhoff's laws, and counting the number of windings around the magnetic field.

Dale
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This is a point which is sometimes not emphasized, but all of circuit theory requires three assumptions:

1) there is no net charge on any component
2) electrical effects happen instantaneously throughout the circuit
3) there is no magnetic coupling between components

When these three assumptions are met (or at least are reasonable approximations) then Maxwell's equations simplify to the KVL and KCL. When these assumptions are violated then KVL and KCL will be wrong.

In a RL or RLC circuit there are indeed magnetic fields within the inductor, but they do not couple to the other components, so the third assumption is still valid and KVL/KCL will work fine.

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With Kirchhoff's laws, and counting the number of windings around the magnetic field.

The problem here with Kirchhoff's laws is that this voltage depends on the path. We can say Vad = VR1 and we can say Vad = VR2, but each gives different results.

mfb
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mfb said:
With Kirchhoff's laws, and counting the number of windings around the magnetic field.
The problem here with Kirchhoff's laws is that this voltage depends on the path. We can say Vad = VR1 and we can say Vad = VR2, but each gives different results.
Don't forget the second part in the quote:
and counting the number of windings around the magnetic field.
This takes the path-dependence into account.

Don't forget the second part in the quote:

This takes the path-dependence into account.

It is a single circuit, so there is only one loop, I can't see how this takes the path into considerations. Any formulas?

mfb
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It is a single circuit, so there is only one loop
Your voltmeter forms another loop, and it is important if the magnetic field is inside this loop.