Why are voltages across a wire in a circuit zero?
They aren't exactly zero, but they are kept as low as possible so that you don't lose power during the transmission of the electricity from one part of a circuit to another.
yes,the voltage across a wire is zero,since its points are considered the same, so the potential difference is zero....
it can be also proved by Ohm's law( V=IR )...the resistance of the conductibg wire is almost zero,then V=0.
Since when is: I times "the resistance of almost zero" equal to zero? Do we have to rethink Ohm's law after all these years?
This is correct....
Another way to think about it is that in a low current circuit the voltage loss in reasonably sized wires is insignificant compared with the circuit element R/L/C etc characteristics.
The voltages are never actually zero but can often be considered negligible in a well designed circuit.
I say often because there are circumstances where the voltage drops along a wire have to be taken into account, even in a well designed circuit.
An example of when they need considering would be building power wiring. Most countries table voltage drops against length of cable in their building codes.
We can usually ignore the drops when the wiring is short. However if the wiring carries a large current as well as a separate small one we must again take the drop into account.
The key elements of circuit theory can be derived from Maxwell's equations. They are NOT exact, they are just very useful approximations that are close enough to correct for a lot of engineering purposes, and they greatly simplify math and design.
One of those approximations is that the voltage at all points on a wire is the same. This is actually two approximations, one is that the resistance of the wire is zero (any nonzero resistance will lead to a nonzero voltage drop per Ohm's law), the other is that the circuit is small relative to the wavelengths involved (otherwise you have to account for the finite speed of light). Both of these are approximations, but are good for typical circuits.
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