# Re: MOT Testing

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• Subject: Re: MOT Testing
• From: "Tesla list" <tesla@xxxxxxxxxx>
• Date: Tue, 26 Apr 2005 09:35:14 -0600
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`Original poster: Steve Conner <steve.conner@xxxxxxxxxxx>`

I saw that business about Z^2=Z1^2+Z2^2+Z3^2+... and I don't know where this came from.

It's used when you are adding complex impedances which is kind of like adding apples to oranges. Except in the strange world of electrical engineering math, one apple plus one orange does not add up to "two fruit".

If you put two 1 ohm resistors in series the result is 2 ohms of resistance.
If you put two 1 ohm inductors in series the result is 2 ohms of "inductive reactance".

`BUT`

If you put a 1 ohm resistor in series with a 1 ohm inductor the result is 1.41 ohms (this is where the formula you saw applies- 1.41 is the square root of 2 which is (1 squared + 1 squared))

This is now a complex impedance though: it's (1+j1)ohms or (1.41< 45deg) ohms. So you may not be able to use it like a regular resistance in any further calculations. In order to know how and when you can apply these formulas you really need some understanding of complex algebra and phasor diagrams. There is an appendix on it in Horowitz and Hill near the back IIRC.

You may be confused by me specifying inductors in ohms when any fool knows they come in henries ::) Provided you are working with sine wave alternating current of a constant frequency, the "reactance" of an inductor in ohms is equal to 2*pi*frequency*inductance. In the example above, to present an impedance of 1 ohm to 60Hz current the inductance should be 2.6mH.

P.S. I can't remember who brought this topic up. But the reason why the voltages across your HV transformer primary and your ballast choke don't add up to the line voltage is also to do with this complex impedance business. If you measured the magnitude and phase angle of each voltage and added them with complex arithmetic, it would all work out. Well if they were sine waves it would, but they are usually crazy waveforms so it would still be wrong.

`Steve Conner`