I'm trying to learn electronics by myself, and I'm starting with simple current calculations. Let's assume we have a straight wire of length L connecting a source and a sink. I know the voltage (V), and for finding the current I need to apply Ohm's law:
$$I = \frac{V}{R}$$
This formula works fine for a DC source, and it's an easy one. What happens when one has an AC system? I saw that the formula changes to:
$$I = \frac{V}{Z}$$
where Z is the impedance, which is a complex number. This formula is a new universe for me because of this complexity. Or at least that's how it looks when trying to learn it.
From this website I saw that one could calculate the impedance at different frequencies, but AC also has to do with magnetic fields as well, right? There are two issues I don't understand yet:
- Why is the impedance a complex number and what does the imaginary number suppose to reveal?
- Is the medium around that wire changing the current calculations due to the magnetic field? If so, how does it get into OHM's law?
I know it might sound stupid to most of you, but for me is not easy to understand.
Best Answer
It's got nothing to do with magnetic fields in a simple situation (skin effect does come into this later but for now ignore it and just learn the basics of impedances). Walk first, then run.
If the load is a resistor then the load impedance = R (or Z = R). So you get a sinewave current with a sinewave voltage and the two waveforms are in sync: -
However, in AC circuits there are capacitors and inductors and these numerically are represented by complex numbers. Simple reason: the voltage current relationship is at 90 degrees. See this for a capacitor: -
And for an inductor: -
So, if you have any inclination about complex numbers this should make sense. If you are a bit rusty on complex numbers then you probably need to do some more research on the topic.
Pictures taken from here and this might be a useful learning resource.