Electronic – Is current calculation in copper wire for AC simple or not

acelectromagnetismohms-lawreactanceresistance

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:

  1. Why is the impedance a complex number and what does the imaginary number suppose to reveal?
  2. 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: -

enter image description here

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: -

enter image description here

And for an inductor: -

enter image description here

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.