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The impedance of an RL circuit is the total opposition to AC current flow caused by the resistor (R) and the reactance of the inductor (X_{L}). The equation for the impedance of an RL circuit is:
where: Z = the total impedance in ohms It is no accident that the equation for impedance looks like the equation for calculating the hypotenuse of a right triangle. Impedance in series circuit is, in fact, often portrayed as a vector diagram where the horizontal side is the resistance, the vertical side is the reactance, and the hypotenuse is the resulting impedance.
The total voltage in a series RL circuit is given by this equation:
where: V_{T} = total voltage
It is very important to notice that the total voltage for a series RL circuit is NOT equal to the sum of the voltages across the resistor and inductor. The sum of voltages in a series RL circuit is always greater than the sum of the voltages across the resistive and inductive components.
Reactance and Impedance Cannot be Directly Measured Although you can use an ordinary ohmmeter to measure resistance, there are no common lab instruments for directly measuring reactance and impedance. For all practical purposes, then, you must calculate reactance and impedance from other circuit values that are more readily available. Step 1. Calculate the value of X_{L} from the known values of f and L: X_{L} = 2pfL Step 2. Calculate Z from the know value of R and the value of X_{L} calculated in Step 1:
Phase Angles in Series RL Circuits It is a basic property of resistors and inductors that their phase angles in a series circuit are always give by: q_{R} = 0º q_{L} = 90º However, there are two equations you can use for defining the total phase angle for a series RL circuit. The total phase angle can be determined by the equation: q where: q_{T} = total phase angle in degrees or radians The total phase angle is also determined by the equation: q
where: q_{T} = total phase angle in degrees or radians The tan^{1}^{ }expression is the inverse tangent which is used for calculating angle q for a right triangle, given the lengths of the two sides.
Secondary Properties of Series RL Circuits The secondary properties of a series RL circuit are the:
Some of these remaining properties are determined from the nature of the components, themselves, and do not have to be calculated. For example, the phase angle for R is always 0º, and the phase angle for L in a series circuit is always 90º. Other values must to be calculated by means of various equations.
Complete Analysis of a Series RL Circuit Here is the procedure for doing a complete analysis of a series RL circuit, given the values of R, L, f, and V_{T}.


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