# Equivalent series resistance

Equivalent series resistance (ESR) is a theoretical device designed to accommodate the real-world limitations of electronic components. The theoretical treatment of devices such as capacitors and inductors tends to assume they are ideal or "perfect" devices, contributing only capacitance or inductance to the circuit. However, all physical devices are constructed of materials with finite electrical resistance, which means that all real-world components contain some resistance in addition to their other properties. An easy way to reconcile this with theory is to express each real-world component as a combination of an ideal component and a small resistor in series, the resistor having a value equal to the unwanted resistance of the physical device.

For example, consider a 10 microhenry (µH) inductor constructed of a coil of copper wire. Suppose the length of wire has a DC resistance of 5 milliohms (mΩ). We can then express this single component as two "perfect" devices: a 10 microhenry ideal inductor wired in series with a 5 milliohm ideal resistor. In this example, the equivalent series resistance of the real-world coil inductor is 5 milliohms.

The physical origins of ESR depend on the characteristics of the device in question. For inductors and transformers ESR is usually just the resistance of the conductor used in the winding. This is the basis for the isolation transformer, which uses the ESR of a simple 1:1 transformer as a safety device to prevent excessive current flow. For capacitors, ESR takes into account plate resistance, leakage through the dielectric, and other factors.

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