# Lumped model of a load and source connected by two long paralel wires

I want to understand how to skecth an equivalent circuit model circuit composed of a load (resistor to make it simple) connected to a soruce bia two long paralel wires. Take the following figure as a reference.

I understand that the coupling of the paralel wires can be modeled as an inductance aswell according to the following formula.

$$\ L_m = \frac{\mu _0 l}{\pi}ln\frac{d-r}{r}$$

How do I represent this incuctance in the equivalent circuit?

To clarify, this cables will also have a partial self inductance and I understand that this L cand be modeled as a series inductance. But I have trouble understanding how to represent the mutual inductance between the two cables.

Would this be a reasonable model?

For the value of M12 I would use the mutual inductance described above L_m

• You do realize that the device is a varistor and that the inductance of the leads is probably irrelevant if you look at the bigger picture. Nov 6, 2023 at 13:42
• Yes! I agree with you. I was pondering it a bout, in general, and sice this is what I have in my desk I used it as an example haha But I also imagine this situation in a bigger circuit, lets say two 10 meter paralel wires between the MOV (or another electric component) and the source. Then the effect would be much greater. Now that I think about it, this latter examplo could have been better xd Nov 6, 2023 at 13:46
• @winny Its true but there can exist resonant effect due to the total inducance and capacitance of the MOV. Eitherway I think I going to remake the question since It doest illustrate my real question in point. Thanks though! Nov 6, 2023 at 13:52
• @winny For clarification, I was refering this effect to surge scenarios. Since the resonance of that low inductance and capacitance combo will happen at very high frequencies. Nov 6, 2023 at 14:17
• The inductance of the loop is the same whether you have a resistor or not. Just as the loop were made from a non-perfect conductor; inductance doesn't care about the conductivity of the wire. Inductance is an area/shape phenomena. Try this loop inductance calculator: eeweb.com/tools/rectangle-loop-inductance Nov 6, 2023 at 16:17