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Considering a charge moving down a wire, the electric field does work on the charges. The work done by the electric field can have two outcomes:it can increase the kinetic energy of the charge carriers themselves or it can be dissipated as heat or other energy forms. I understand that the potential difference between two points is the difference in the electrical potential values down which the electrons move. However this is clearly distinct from what we can measure with a voltmeter across these two points, as we will not measure an energy difference for the stored energy that became the kinetic energy for the electrons.

I realise that when the current is constant (kinetic energy of electrons not changing), the voltmeter measurement will be the same as the difference in electric field potential between the two points. For any direct current circuit, the time it takes for the drift velocity/constant current to be reached is negligible so we can assume the voltmeter measure the exact potential difference.

My questions are:

  • is there a difference between potential difference & voltage? I am thinking that maybe potential difference refers to the actual difference in potential and voltage is the potential difference minus the amount of energy that goes into increasing the kinetic energy of the electrons per jnit charge. Therefore voltage would be what we measure with a voltmeter.

  • mu second question is a out how this would work for alternating current circuits. Surely then as the kinetic energy of the electrons keeps changing the voltages would not be reflective of the potential difference?

Hope my question makes some sort of sense...

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Potential difference and voltage are the same. Potential difference is more useful term because you can only really talk about voltage relative to another potential - hence potential difference.

The "voltage" in an AC circuit is constantly changing, and so is the electric field felt by an electron and so is the electron's energy

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The electric potential difference, often denoted as $V$, is synonymous to voltage. You may confuse electric potential with potential energy, which has the units of energy. The names are similar because there is a connection: the electric potential is just the potential energy per unit charge.

To put it in concrete terms, in order to move a particle with charge $q$ from point $a$ to point $b$ with potential difference $V_{ab}$ between the points, the energy one must spend (i.e. the potential energy between the points) is given by $W_{ab} = q V_{ab}$.

In a metallic conductor, the potential difference between to points in a piece of wire does not, however, lead to corresponding increase in the kinetic energy of the electrons. This is because, as the electrons move, they constantly hit impurities of the lattice in the conductor. The kinetic energy that the electrons gain between the collisions from the electric field is transferred into those impurities and becomes heat. This is why your computer gets hot and needs cooling to operate.

In an AC circuit, the electrons indeed keep moving back-and-forth as they respond to the changing electric potential. The number that voltmeters show when you plug them into and AC circuit can be either the peak voltage (i.e. the absolute value of the maximum of the voltage as it periodically changes) or the average of the square of the voltage (i.e. $\bar{V} = \frac{1}{T}\int_0^T V(t)$, where $T$ is the length of the period).

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