# Equivalent Circuit Diagram for a Coil

In addition to its inductive reactance, every real coil also possesses an active resistance (due to the wire it is made of) that is dependent on the material used for the wire and its length (i.e. the number of coil windings). Consequently, a real coil can be represented by the following equivalent circuit diagram in the form of an ideal coil of inductance *L* connected in series with an active resistance *R*_{V}.

The phase displacement between the current and voltage of a real coil is therefore not exactly 90° but somewhat less, as given by the ratio between the active resistance *R*_{V} and reactance *X*_{L}. The diagram below shows the related voltage and current vectors.

Including ohmic coil resistance in an analysis of RL high-pass elements yields the circuit shown below.

Compared with the ideal component considered earlier, this real high-pass element has a slightly different frequency response. Due to the coil's active resistance *R*_{V}, a DC voltage supply (i.e. frequency of 0) causes the high-pass filter to output a voltage slightly higher than 0. Consequently, the amplitude at low frequencies no longer tends to precisely 0 but to a slightly higher value. The following diagram (upper part) illustrates this (note that the amplitude axis has a scale in dB). For comparison, an ideal high-pass characteristic is represented in dashes. The phase response (lower graph) also changes, the initial phase at low frequencies now being 0° instead of 90°. In other words, the phase angle initially rises and drops again toward zero as the frequency increases.

A change in frequency response also changes the high-pass cut-off frequency as follows:

If *R* > 0.5·*R*_{V}, a condition existing in practically all real cases, the real high-pass element's cut-off frequency becomes larger than the ideal RL high-pass element's, where *R*_{V} = 0.