Introductory physics: voltage

What exactly is voltage? If you ask an engineer, she will probably tell you that voltage drives electric current. And so it does – but what is it? What is its nature? ‘Some sort of energy‘, you might expect. And so it is, although the technical answer is that voltage is electric potential energy per unit charge.

In physics, energy is simply the capacity to do work. Potential energy is the expression we use to convey the fact that an object can have energy simply due to its position or configuration;  a stretched rubber band will do work if released (snap back), as will a compressed spring (spring out), or a brick held aloft (fall on someone’s toe). Indeed, students usually encounter potential energy first in the latter context; any object lifted to a height in the earth’s gravitational field acquires potential energy equal to the amount of work done to get it to that point.  Plus, if you remove the restraint holding it in place, the object will fall and do precisely this amount of work on the ground as it lands (all of its original potential energy is converted to kinetic energy). So you can think of potential energy as work waiting to happen.

A lifted object has potential energy because work was done to get it there; this energy is converted back to work if it is released

Last week, we saw that any electric charge sets up an electric field which will repel like charges and attract unlike ones. Hence it takes work to bring a test charge into the field of a like charge so if we do this we give it electric potential energy ( if you remove the restraint, the charge will rush away). The amount of work done and hence the potential energy acquired will depend on the size of the charge you bring up, so we define instead the electric potential energy per unit charge, also known as the potential. To be strictly correct, potential should be measured relative to something, so physicists talk of potential difference, defined as the difference in potential between the point in question and zero field. Since energy is measured in joules, potential is measured in joules per coulomb or volts and hence potential also became known as voltage. So voltage, potential and potential difference are all the same thing.

In a battery, a potential difference is maintained between the terminals. Charge cannot flow from one terminal to the other because they are not connected. However, if a conducting path between the terminals is provided (by connecting them by wire), a current will flow in the circuit.

A battery and circuit (tnote that the direction of current is defined as the direction +ve charge would move for historical reasons)


Since voltage is defined as energy per unit charge, it should be obvious that the product of voltage and charge is energy (or work)  i.e.  W = qV. Thus if a charge of 1 Coulomb is moved through a potential difference of 1volt, 1 joule of work is done.

However, the charge on a single electron is not 1 Coulomb, but a minute 1.6E-16 Coulombs. Hence in the world of particle physics, one typically deals in tiny, tiny amounts of energy. For convenience, we define the unit electron-volt (eV) as the work that is done when a single electron moves through a potential difference of 1 volt.


How many eVs  there are in 1 Joule of energy? The maximum energy achievable at the Large Hadron Collider (LHC) in Switzerland is 14 TeV – show that this corresponds to only 2.2 microjoules of energy. (Note that although this is a small amount of energy, the energy density is enormous because the cross-sectional area of the colliding particle beams is extremely small).

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4 responses to “Introductory physics: voltage

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  2. In particle physics, we have a unit of energy that ties in nicely with the concept of potential energy that you describe here. If you think of a potential difference of one Volt set up by a battery connected to two plates, and you somehow move an electron or a proton from one plate to the other *against* that potential, then that electron or proton has gained an energy of one “electron Volt” or “eV” for short. When we talk about the beam energy of the protons in the Large Hadron Collider (LHC) as being 7 TeV, that means that each proton has gained 7×10^12 (i.e., 7 million million) eV! Clearly, this cannot be achieved with batteries. ;)

  3. cormac

    Thanks Micheal – that’s such a good point I think I’ll put something on it on the post!

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