# Voltage drop in an electric circuits

• John Pang

#### John Pang

I don't understand why the voltage drops only when the charges in an electric circuitnpass through resistors or electric devices, but don't drop as charges move through the wire. As charges move through the wire due to electric potential differences, from a high potential to a low potential, the electric potential differences should drop across the distance.

An ideal wire has no potential difference across it since it has no resistance.
Real wires are modeled as an ideal wire in series with an ideal, but very small, resistance.

This means there will be a paradox when you draw an ideal wire connecting the terminals of a battery... but ideal wires make good approximations to the wires in real circuits because a wire typically has a very low resistance compared with the load.

John Pang
I don't understand why the voltage drops only when the charges in an electric circuitnpass through resistors or electric devices, but don't drop as charges move through the wire. As charges move through the wire due to electric potential differences, from a high potential to a low potential, the electric potential differences should drop across the distance.
We all understand your dilemma on this. Instead of a battery, use a constant current source, giving, say, 1 amp of current whatever is connected to it. Now connect you wire across the terminals of the source. As the electrons move so easily in the wire, it takes very little potential difference across it to drive them through. A voltmeter connected across the wire will give a very low reading.
When you use a 1.5 volt battery, it cannot provide the thousands of amps necessary to create 1.5 volts potential difference across the wire because the electrons move so easily.

John Pang
Real conductors have non-zero resistance and will have non-zero voltage drop. Copper itself has a resistivity of 1.8x10-8 ohm * meters and you can measure this voltage drop with a simple undergrad lab experiment like the one my E&M class performed a month or two back.

John Pang and Dale
it is best to stte that the voltage drop across connecting wires is negligible. very much smaller than other voltages in the circuit...usually.
it is somehow 'wrong' to say that it is zero

Not really - the "wire" in a circuit diagram is defined as having zero resistance, just like electrostatics is taught with zero resistance "conductors" and ballistics is taught with "negligible" resistance air ... it is usually understood not to be a real wire in the same way that a wiggley line is not a real resistor. Later students should realize that real loads are reactive too, not just pure resistances. We use circuit diagrams to model real world situations, they are not supposed to be exactly the same.

Although there are usually exercises in which the non-zero resistance of real conductors is involved, this is not usually made clear in secondary school textbooks ... or even at junior levels in college... so I usually have to spell it out when students do linear network theory and equivalent circuits. Once they get it I can use ideal circuit components to model things like transistors and op-amps.
It is easy to confuse the map for the territory when nobody tells you it's just a model.

We use idealizations in physics all the time. Spelling out all the caveats all the time would lead to too much writing.
This is why context is important.

I personally like to look at the units of Voltage, which is Joules per Coulomb. In words, it is saying how much energy is required to move a certain number of electrons (recall that each electron is roughly 1.602 x 10-19 C) from one spot to the next; this is why the voltage across an ideal wire should be zero.