# Phase Angles and Complex Numbers

#### lendo1

Joined Apr 24, 2010
34
So Chapters 3 and 4 of the E-book (which is a fantastic resource by the way, thank you to the developers!) deal with inductive and capacitive AC circuits.

The physics of inductive and capacitive responses to AC makes perfect sense to me, as does this statement from the chapter:

"For the resistor and the inductor, the phase relationships between voltage and current haven't changed. Voltage across the resistor is in phase (0o shift) with the current through it; and the voltage across the inductor is +90o out of phase with the current going through it. We can verify this mathematically"

Ok, the voltage across the inductor leads the current, and the voltage across the resistor is in phase with its current. Well, what exactly does the total current, and more importantly the phase angle of the total current, tell us about the circuit? If the voltage and current through and across any component will be just a property of that component, what does it mean to have a total current of 5 amps at an angle of -35 degrees? Is this just an abstraction, or would current in a 0 resistance/reactance part of the circuit actually be lagging behind the voltage source waveform at any given time? Oh, and why?

#### t_n_k

Joined Mar 6, 2009
5,455
.... what does it mean to have a total current of 5 amps at an angle of -35 degrees?
The phase angle of -35 degrees would normally indicate the angle of the current waveform in relation to the supply [source] voltage waveform.

So in this case the circuit current would apparently lag the supply voltage.

If this were (say) in reference to a series RLC circuit driven by an AC source then the individual components would have the anticipated phase relationship between the current and their respective terminal voltages. The current would lag the inductor voltage by 90°. The resistor voltage would be in phase with the current. The current would lead the capacitor voltage by 90°. If one were to take the vector [or complex] summation of the three individual component [VR, VL & VC] voltages, they would add to a value equivalent to the source voltage in terms of both magnitude and phase.