accircuits2

accircuits2 - Complex Numbers and AC Circuits We pretend...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Complex Numbers and AC Circuits We pretend that there is an (imaginary) number, i , which, multiplied by itself, equals &1: 1 i (1) A so-called complex number, z = x + iy , has both, a real part (Re( z ) = x ) and an imaginary part (Im( z ) = y ). The complex conjugate z * of z one obtains by flipping the sign of all terms with an i in them, i.e., z * = x & iy . Leonhard Euler (1707 & 1783) discovered the relation, which relates complex numbers to the (periodic) trigonometric functions (and which is the reason why we are doing what we are doing!): α sin cos + = i e i (2) Consider the voltage U(t) that appears somewhere in some AC circuit. This is a periodic function, so it makes sense to try to write this as t i e U t U ω = 0 ) ( (3) This is a complex number, but instead of specifying its real and imaginary parts, we specify its amplitude U 0 and its phase ω t . Here, ω is the angular frequency, which is related to the frequency f by ω = 2 π f . When we have any complex number
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

accircuits2 - Complex Numbers and AC Circuits We pretend...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online