In a circuit with an ideal coil, that is parallel to a resistor, what is the overall resistance of the circuit? If you do the law of resistances in parallel circuits I get 0. However, I don't think that can be right, since there is a resistance inside of the circuit. Then how can the overall resistance be 0

  • $\begingroup$ AC or DC voltage? $\endgroup$
    – Gert
    Commented Apr 27, 2021 at 16:37
  • $\begingroup$ Draw the circuit you are describing. $\endgroup$ Commented Apr 27, 2021 at 17:10
  • $\begingroup$ DC. The circuit circuit just consists of an ohmic resistor parallel to an ideal coil $\endgroup$
    – Octot
    Commented Apr 27, 2021 at 17:19
  • $\begingroup$ resistance is zero but the impedance is not zero. it is a function of frequency. $\endgroup$
    – user45664
    Commented Apr 27, 2021 at 17:25

2 Answers 2


Assuming that by "ideal coil" you refer to a purely inductive coil with an ohmic resistance R = 0, you can assume that, for the purposes of calculating total resistance, the coil is simply a short-circuit that bypasses the resistor in parallel. Computing the parallel resistance gives R(parallel) = 0, which is indeed what you arrived at!

However, do bear in mind that the above is applicable in the case of a DC circuit only. If the circuit was to carry AC, the impedance of the inductive coil would matter (recognise that Z = Lw for an inductor with inductance L and angular frequency w). In a DC circuit, the angular frequency is 0 so the overall impedance of your coil is 0!

So ultimately, the answer to your question depends on what type of circuit you are dealing with. If DC, you are absolutely right to say the resistance is 0 effectively.


The opposition to the flow of current by an electrical component is due to its electrical impedance. Impedance is the broader term and applies to capacitors and inductors, as well as resistors. Pure resistance is a special case of impedance.

For your parallel combination of an ideal inductor (having no "resistance") and an ideal resistor (having no inductance), if the resistance of the resistor was, in fact, zero, then the resistance of the parallel combination would also be zero. But its impedance is only theoretically zero if you are dealing strictly with DC voltage sources. That is because the inductor has impedance if the source is AC and the resistor can have some self inductance for AC sources if the frequency is high enough.

Hope this helps.


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