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# Phase Shift in an RL Element

An ideal coil comprises a pure reactance *X*_{L} where the voltage leads the current by a phase angle j = 90°, the two vectors thus forming a right angle (illustrations on the left below). Connecting an ohmic resistance and inductance in series to form an *RL element* produces, as in the case of the RC element considered earlier, an overall resistance comprising an active and a reactive component. In this case, the voltage leads the current by a phase angle j that lies somewhere between 0° and 90° depending on the frequency, resistance and inductance (illustrations on the right below). The voltage vector *U* here is determined by geometric addition of the partial voltages *U*_{R} (in phase with the current) and *U*_{L} (leading the current by 90°).

The following diagram shows the triangle of resistances for an RL element.

The impedance *Z* can be calculated easily from the triangle of resistances, which being right-angled, results in the following relationship:

Replacing *X*_{L} with the relationship derived earlier results in the following:

The phase angle j can also be determined from the triangle of resistances:

If the values of w or *f*, *R* and j are known, this equation can be used to determine inductance by resolving in terms of *L*. The following relationship is then obtained:

Alternatively, the phase shift between the coil voltage *U*_{L} and supply voltage *U* can be measured. The inductance is then derived from the following formula: