AC Components and Circuits
Series RL Impedance
If you know the values for R and X_{L}, you can solve the equation directly. In most practical situations, however, you know the values of L and f, and must calculate X_{L} in order to use the seriesZ equation. Since this is a series circuit, the magnitude of the current is the same at all point. It's the voltage that is subject to phase shifting. Recall there is no phase shift for a resistor (q_{R} = 0º). And for the inductor, the voltage is always leading the current by 90º ( q_{L} = 90º). It is the phase of the total circuit impedance ( q ) that varies between 0º and 90º.
Examples Endless Examples & Exercises
Voltages in Series RL Circuits A series RL circuit is a simplelooking circuit. In most respects, it looks similar to a series resistor circuit that is operating from an ac source. But something very interesting happens when you measure and compare the rms voltages across the resistor and inductor—the sum of those two voltages is greater than the source voltage! Suppose you measure the ac source voltage (V_{T}) and find it to be 18 V. Then you measure the voltages for V_{R} and V_{L}, and find them to be 6 V and 17 V, respectively. How can that be? 6V + 17V is a long way from 18V This apparent discrepancy is caused by the fact that the ac waveforms across the resistor and inductor are out of phase. The phase diagram shows that the voltages across the two components are 90 out of phase, with the inductor voltage leading the resistor voltage. The total voltage is not the sum of the resistive and inductive voltage, but rather a level determined by the length of the VT vector:
And, yes, that is a variation of the Pythagorean Theorem
In actual practice, it makes more sense to measure V_{T} with a meter or oscilloscope than to calculate it. The real value of the equation is that it explains how the total voltage in a series RL circuit is not the sum of the voltages across the components. Secondly, the equation can be rearranged to deal with calculations where you know the total voltage and the voltage across one of the other components:
Exercise V_{R} = 12.6V V_{L} = 8V
q = 32.4º
Currents in Series RL Circuits
Analysis of Series RL Circuits
Students who are new to the procedures for analyzing circuit often ask, "How do you know where to start? How do you know what to do next?" The answer is simple and so very true: Do whatever you can do with the data that is available. Endless Examples & Exercises
I and V Phase Relationships
Variation of Z with Frequency
Variation of Phase Angle with Frequency


David L. Heiserman, Editor  Copyright © SweetHaven
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Revised: June 06, 2015