How to calculate voltage drop in conductors? 2

[davidd31415]

I've been using this 'nomograph' to estimate voltage drop in conductors:

http://www.kepcopower.com/nomomax.gif

How would I calcualte voltage drops with equations? Is this something burried in Maxwell's equations?

Thanks

 

[MacGyverS2000]

V=IR

Plug in the current and resistance per foot of the wire. Were you looking for something more magical?

Dan - Owner

http://www.Hi-TecDesigns.com

 

[btrueblood]

You can also correct the resistance value for temperature, and (if really ambitious) do a heat-transfer analysis to find the rise over ambient for the power dissipated within the wire...

 

[IRstuff]

Actually, I'm a contrarian and prefer V = RI

TTFN

FAQ731-376

 

[jimgineer]

Maxwell's equations don't tell you much at the 'macro' scale unless you have some very specialized software and/or the ability to model differential equations (and to set up equations that represent what is really going on at the 'micro' level of a conductor.

However, V=IR will suffice as long as you have for example a uniform cross section conductor with uniform resistance.

Only think of applying Maxwell's equations when you need to model the electrical properties of something in relation to the geometric properties.

Resistance is a scalar abstration that allows you to not have to 'mess' with Maxwell's equations at all.

 

[dpc]

If these are ac circuits, you might want to think in terms of V = IZ and use the phasor quantities.

 

[davidd31415]

Ok,

How about resistance per length as a function of wire diameter? How can I calculate that?

 

[geekEE]

The formula for resistivity can be used to calculate the resistance. Just plug in the resistivity of copper (or aluminum as the case may be).

http://en.wikipedia.org/wiki/Resistivity

Glenn

 

[IRstuff]

There are tables with the values already calculated:

http://www.radiolocman.com/shem/shem-cache.html?di=18899

http://www.mogami.com/e/cad/wire-gauge.html

TTFN

FAQ731-376

 

[waross]

Right on dpc;
Most of us are able to calculate the resistance of a conductor carrying DC, and from that the DC voltage drop.
Most of us use the tables for AC voltage drop.
Resistance is not the only factor affecting the voltage drop in an AC conductor. The tables account for the other factors under defined conditions. The voltage drop may vary with the power factor also in an AC circuit.
Use the tables.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[davidd31415]

GeekEE,

Thanks that's what I was looking for.

IRstuff,

Thanks for the table links. I'll remember they're in this thread.

 

[Truemanator]

I was worried there for a second. I saw the topic and question and thought, "Doesn't V ALWAYS equal IR?"

Thank goodness I've learned something in 3 1/2 years of school.

 

[waross]

V=IZ.
Regulation does not always equal the voltage drop in the conductors.
That is to say: the voltage at the load does not always equal the voltage drop in the conductors arithmetically subtracted from the supply voltage.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[Clyde38]

Is high frequency involved?

Excerpt from ePanorama.net

Skin effect

Skin effect is an effect that the electricity in high frequencies does not use the whole conductor area. High frequencies tend to use only the outer parts of the conductor. The higher the frequency, the less of the wire diameter is used and higher the losses. Sin effect must be taken care in high frequency coil designs.
The frequency dependency of the resistance of a cylindrical conductor can be calculated by the following formula, which is surely valid for high frequencies and radii of approx. 50 um:
R(f) = R(DC)* (1 + 1/3 * x^4) with x = Radius/2*sqrt(pi*frequency*permeability*conductivity)
The "formula" for skin effect is the same whether the conductor is rectangular or cylindrical. That is why the same value of "radius" used in wire size in a switch mode transformer is used to determine half the thickness of a flat foil conductor in the case of foil-wound secondary’s.
An approximate equation for the resistance ratio for rectangular conductors (from Terman) is:
rho = 1/(((8PI * f)/(Rdc * 10^9))^0.5)
Skin depth is not an absolute, but only the depth where current through the wire or foil has fallen to a specific proportion of the current at the surface. In fact, current falls off exponentially as you move inward from the surface. The depth of the "skin" is also influenced by proximity to nearby conductors (such as in a transformer) so is itself not absolute. Also the formula has to be modified if you use wire that is ferromagnetic (iron for example).
In addition to skin effect a lot of engineers doing their own magnetic design don't consider the 'proximity effect' which 'crowds' the current to one side of the conductor and increases losses. This condition is worst in thick multi-layer windings. Fortunately, many of the new transformer shapes have a long and skinny window - good for low leakage L and low proximity effect losses.