Before starting this module, you should be able to:  When you complete this module, you should be able to: 
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Topic 72.1 Impedance of a Series RL Circuit
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.

In a series RL circuit, R = 100 W and X_{L }= 150 W. What is the total impedance
of this circuit? Ans: 180 W 
Topic 72.2 Voltages in a Series RC Circuit

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. 
What is the total voltage applied to a series
RL circuit when the voltage drop across the resistor is 12 V and the voltage across the
inductor is 10 V? Ans: 15.6 V 
D 
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.

Procedure
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:

Given a series RL circuit where R = 20 kW, f = 220 kHz, and L = 10 mH,
calculate (a) the inductive reactance and (b) the total impedance. Ans: (a) X_{L} = 13.8 kW, (b) Z = 24.3 kW 
Topic 72.3 Phase Angles of Series RL Circuits

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.
where: q_{T} = total phase angle in degrees or
radians
where: q_{T} = total phase angle in degrees or
radians 
The
total phase angle of a series RL circuit is always somewhere between 0º (purely
resistive circuit) and 90º (purely inductive circuit). 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.

A series RL circuit has values of R = 120 W and X_{L}
= 150 W. Calculate
the phase angles for R, L and the total circuit. Ans: 0º, 90º, 51.30º 
What is the phase angle for total voltage and
current in a series RL circuit where R = 10 kW, L = 100 mH, and f = 30 MHz. Ans: 62º

Topic 72.4 Analysis of Series RL Circuits
P 
Secondary
Properties of Series RL Circuits

A complete
analysis of a series RL circuit usually proceeds from knowing the values for R, L, f,
and V_{T}. The analysis then amounts to determining the remaining secondary
properties of the circuit. 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. 
P 
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}.
