Imaginary Numbers in Electricity

Date: 07/31/98 at 19:03:42
From: Luis A. Munoz
Subject: Imaginary numbers in AC analysis

I'm a student of electronic engineering, and I'm learning about  
capacitance and inductance in a circuit. The analysis of this kind of 
circuit uses a number i = sqrt -1. Why is it needed? What is the 
imaginary plane?

Date: 07/31/98 at 21:23:14
From: Doctor Jeremiah
Subject: Re: Imaginary numbers in AC analysis

Hi Luis.

I am an electrical engineer and so I can tell you that there are often
more imaginary numbers than real numbers in electrical problems.

As you know, a complex number is a pair of numbers where one of the 
numbers is a real number (a member of the real number set) and one of 
the numbers is imaginary (a real number multiplied by the value i 
which is defined to be the square root of -1).

Imaginary numbers are not imaginary. They just do not belong with the 
group of numbers that we named "the real number set."

When electricity flows through an electrical circuit component like a 
light bulb that resists the flow of electricity by using some of it to 
do work, the current flowing through the bulb is purely real and can 
be measured by a current meter accurately.

When electricity flows through other devices where no real current can 
go, the current flowing through that device is purely imaginary. If it 
were measured the current flow through the device would show zero 
because a meter can only measure the real part of the current.

Think of it like this: a coil is just a wire, so if you run electricity 
through it there is no real voltage drop because there is no real 
resistance. A capacitor is just two pieces of metal that do not touch 
so if you put a voltage through it no real current can flow.

- Doctor Jeremiah, The Math Forum
  http://mathforum.org/dr.math/