# Is there any way to determine how long a wire is?

This is for transmission lines applications. Are there any way to know how long the wire like by getting the resistance of the wire(but how). Or is it possiblee to charge the wire until it produces arcs then messure the value of the resistance of the wire by using it. Or by the "ringing" after it disconnects.

• Several companies make TDR (time domain reflectometer) equipment. A small step above standard hand-held test equipment, but not that expensive. – Jon Custer Jan 3 at 17:05

You can obtain the length from electrical resistance if you know the diameter of the wire (supposing it has circular section) and the material`s resistivity.

If the wire has constant transversal section of area $$S$$, length $$L$$ and it has electrical resistivity $$\rho$$ then its electrical resistance is

$$R = \frac{\rho L}{S}$$.

Then you can measure its electrical resistance $$R$$ (preferably under a direct current, as it may be different in alternating currents; but then an multimeter or ohmmeter can be used). If you know its diameter, compute $$S$$; if you know the material it is made of you can search for the value of $$\rho$$. Then all you have to do is to solve for the above equation and get $$L$$.

If you don't know the material of the wire but you can measure the resistance $$R_0$$ of a short exposed portion of length $$L_0$$, then by using the above formula it can be seen that $$R$$ is proportional to $$L$$, thus:

$$\frac{R}{L} = \frac{R_0}{L_0}$$,

then

$$R = R_0 \frac{L}{L_0}$$.

The arc method wouldn't work because arcing voltage doesn't depend on the wire length, but rather on its thickness. Anyway, you shouldn't try to charge the wire until it is arcing; besides for the obvious security problem (using high voltages can get you electrocuted), this method when applied in air is not reliable even a bit.

The dielectric strength of air is not at all fixed or stable. You can forget about the often quoted value of $$3 \cdot 10^6$$ V/m; that works for perfectly clean air. Normally the air is not clean, at least because it contains ions and electrons caused by radiation from the ground, rocks, buildings etc. and also by pollution of the air; there are other impurities in the air too. That means the actual dielectric strength of air may be far smaller than the above value. And if you slowly charge the wire you may actually lower the dielectric strength of surrounding air by multiplying ions and electrons around the wire. This is because existing electrical charges in the air get accelerated near the charged wire and they bump into surrounding air molecules, ionizing them and thus producing even more charges.

This method is not good for measuring. And the end result may be that you get a potentially lethal electric shock, even if you stay farther away from the wire. It is very easy to underestimate the distance at which you get electrocuted and actually be too close to the wire when you think you are at a safe distance.

As a final warning, always avoid using dangerously high voltages. Do not go above 8-10 volts if possible. Even those can be dangerous if you have wet hands or a heart disease. Best go with 1.5 volts, the standard battery voltage. Measuring the length of a wire (inside a coil for example) by electrical means can be done with low voltages or with dedicated instruments.

• Note this will only work if you have access to both ends, either by having a return wire or by having it on a spool. – Chris Stratton Jan 4 at 7:20
• if you have a return wire then you know how long the first wire is. – user45664 Jan 4 at 18:06