Lessons · Engineering · Why alternating quantities are drawn as arrows
Why alternating quantities are drawn as arrows
An alternating voltage or current is a sine wave with a size and a timing. A phasor is an arrow that carries both: its length is the size, its angle is how far ahead or behind it runs. Adding two sine waves by arithmetic is hard; adding two arrows is geometry.
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In beta. This lesson was written for Hone and has not yet been checked by a licensed engineer. Practice material, not professional advice. What that means.
What it is for
Every AC circuit, meaning alternating current, has quantities that peak at different instants, and adding their peaks is simply wrong. Phasors exist so that timing is carried through the sum instead of being thrown away.
How to think about it
Before adding anything in an AC circuit, ask whether the two quantities peak together. If they do, add the numbers. If they do not, they add as arrows -- which for a right angle means the square root of the sum of the squares, not the sum.
Worked example
A sine wave has a size and a timing.Both matter downstream.
A phasor carries both: length and angle.One arrow per quantity.
In phase: add the lengths.Ordinary arithmetic.
At right angles: root of the sum of squares.Which is always less than the plain sum.
Your turn
Two quantities at right angles, 3 and 4. Write their phasor sum.
sqrt(3^2 + 4^2) =
Solve one, graded on the server
The trap
Adding the numbers when the quantities are out of step. Three and four give seven only if they peak together; at a right angle they give five.