XL3Ω, then the complex impedance is 0 j3, and is at the point (0, 3) on the RLplane. These points, and others, are shown in Fig. 13-6.In real life, all coils have some resistance, because no wire is a perfect conductor.All resistors have at least a tiny bit of inductive reactance, because they take up somephysical space. So there is really no such thing as a mathematically perfect pure resis-tance like 5 j0, or a mathematically perfect pure reactance like 0 j3. Sometimes youcan get pretty close, but absolutely pure resistances or reactances never exist, if youwant to get really theoretical.Often, resistance and inductive reactance are both deliberately placed in a circuit.Then you get impedances values such as 2 j3 or 4 jl.5. These are shown in Fig. 13-6as points on the RL plane.Remember that the values for XL are reactances, not the actual inductances.Therefore, they vary with the frequency in the RL circuit. Changing the frequency hasthe effect of making the points move in the RL plane. They move vertically, going up-wards as the ac frequency increases, and downwards as the ac frequency decreases. Ifthe ac frequency goes down to zero, the inductive reactance vanishes. Then XL0, andthe point is along the resistance axis of the RL plane.Vectors in the RL PlaneEngineers sometimes like to represent points in the RL plane (and in other types of co-ordinate planes, too) as vectors. This gives each point a definite magnitude and a pre-cise direction.Vectors in the RL Plane23513-5The RL quarter-plane.