How can the electric potential be constant between two points in a wire?

[du_768]

Homework Statement: circuits - terms
Relevant Equations: -

How exactly can the electric potential be constant between two points in a wire; (assuming that it is electron current); if the electron is moving from a region of high electric potential to a low electric potential because of the terminals, shouldn’t the electric potential of the electron be decreasing regardless as it travels through the wire because its becoming closer to the positive terminal? I learnt that when an electron moves towards a positive plate its electric potential is decreasing?

 

[.Scott]

If there is an electric current across a resistor, then there is an electric potential between those to points.
That said, the resistance across a copper wire is pretty low. So the potential across a short copper wire will be very small even with fairly high currents.

 

[Borek]

shouldn’t the electric potential of the electron

Potential is not a property of an electron, but of a point in the field.

But: yes, each individual electron moves in the direction determined by the field gradient. However, it gets replaced with another electron, so the system is in a steady state - current flows, electrons move, but at every given point in time potential field and the number of electrons in any place remain constant.

 

[du_768]

Potential is not a property of an electron, but of a point in the field.

But: yes, each individual electron moves in the direction determined by the field gradient. However, it gets replaced with another electron, so the system is in a steady state - current flows, electrons move, but at every given point in time potential field and the number of electrons in any place remain constant.

wait so is it correct that at each point in the circuit in the wire, there is an associated electric potential at that distinct point? so when current flows, when one electron gets 'pushed' into the wire, another electron gets pushed out at the same time, so the electric potential energy each electron is decreasing as it is getting pushed towards the positive terminal?

But in my textbook, it says that if you place a voltmeter at two points in a wire (with no other component), the voltage would be 0? How does that make sense, if the electirc potential energy would be decreasing as it goes towards the positive terminal, and therefore the electric potential is decreasing — so there is a difference in electric potential?

 

[Borek]

Ohmic drop iR is present always where there is the current and the resistance - so it is present in every real conductor. Think about voltage divider made with resistors 50kΩ and and 50kΩ - at its central point it divides the applied voltage in half. What if you replace resistors with 5kΩ? 5Ω? 0.00005Ω? Does the divider stop to work? (at some point it probably evaporates, but that's another thing )

For good conductor ohmic drop can be way too low to be measurable with a voltmeter though, so in most circuits assuming voltage is identical at every point of the wire is a reasonable approximation.

 

[Babadag]

As it is already explained, the potential of a point is the voltage drop from a point considered as origine up to the considered point. Since the voltage drop equals to the product of current by impedance, if current is constant and impedance also then the point potential is constant. The impedance presents two components:
the resistance and the reactance. The resistance depends-merely-on conductor temperature and the reactance, as a part of entire circuit, depends on relative position of this part vis-a-vis to the rest of the circuit.
In the microscopic world, if we consider the electron as a sphere of negative charge, circulating free in the conductor, in which an electric field exists, and considering this field as a force, then, according to Newton, the electron will accelerate.
However, the conductor is not an empty conduit [or a pipe], but it is filled with milliards of atoms oscillating around a fix point. This oscillation, due to heat, produced an opposition force, and so the electron losses the acceleration and circulate with a limited speed. This force represents the conductor resistance.
If we consider all the electrons forming a stream of electric charges-the current- a variable density-charge per local area-it could be defined and the electric field in any point is E=ρ*J where ρ it the specific resistivity in this point producing a current density J. The voltage drops between two points equals to E*distance -if E is constant- or equals to integral of E*dr if ρ or J [or both] is variable.

 

[sophiecentaur]

But in my textbook, it says that if you place a voltmeter at two points in a wire (with no other component), the voltage would be 0? How does that make sense

It makes sense when you are making an engineering measurement with real equipment and in appropriate circumstances. ~~~No wire is ideal but it can be treated as such when it's of the right material and not too thin. Your book is talking about a Voltmeter and not a 'nanovoltmeter'.