Introductory physics: the relation between voltage and current

We have established that voltage is simply energy per unit charge (see last post). What then is current and how does it relate to voltage?

Electric current is a flow of charge, just as a river current is a flow of water. By definition, an electric current I is the amount of charge q flowing per second, hence I = q/t . Current is measured in Colombs per second (also called Amperes, see below). However, we noted last day that the charge on the electron is only a tiny fraction of a Coulomb – hence a current of 1 Coulomb per second corresponds to an awful lot of electrons running around. (How many?)

The lamp lights because the current goes through it to complete the circuit

Since charge will only flow if there is a voltage difference between the terminals of a circuit (last day), you might expect that there is a simple relation between voltage and current. In fact, the German scientist Georg Ohm was the first to discover that there is a linear relationship between the two in many materials. Ohm’s law states that the current I passing through a material connected to an energy source V is given by the equation I = V/R. Here, R is the constant of proportionality and is called electrical resistance and you can see why from the equation: a material with a very large value of R will pass almost no current (electrical insulator), while another material with very small R will yield a large current for the same voltage (good electrical conductor).

Many materials have a linear relation between voltage and current – the slope of the graph is the material’s resistance


1. Ohm’s law is a bit of a misnomer – it is not a universal law of physics but simply a property of some materials (many materials have a nonlinear response to voltage, including your cat)

2. Current can be considered a fundamental physical quantity in its own right and indeed the ampere is defined as a fundmental unit (see here). However, it’s much better to define it in terms of electric charge, since this is more fundamental.

3. Some unfortunate people quote Ohm’s law as V = IR and play silly games with triangles. In my opinion, I = V/R conveys the physics of the situation much more clearly.

4. It seems from Ohm’s law that a material with zero resistance could pass infinite current! No such materials are known, but some materials have extremely low resistance at very low temperatures – known as superconductors. A good application of superconductivity can be found at the Large Hadron Collider, where protons are guided around the ring by magnets made of superconducting material: this reduces power consumption enormously but the snag is that the experiments have to be done at at extremely low temperatures.


Filed under Introductory physics

23 responses to “Introductory physics: the relation between voltage and current

  1. An earlier (and probably the first) use of superconducting magnets at a particle accelerator was made at Fermilab (located in Illinois, USA). The superconducing dipole magnets was once dubbed “The Energy Doubler” because you could get an accelerator with twice the collision energy for the same amount of power (i.e., money paid to the electric power companies). A student might wonder why we have to pay any bills at all, if the resistance is zero? Answer: it takes power to run the refrigeration units that cool down the conductors so that they attain the superconducting state. The cost for doing that is much smaller, currently, than it would take to produce powerful magnets with ordinary conductors.

  2. cormac

    Yes I know, but it’s geting a little way from Ohm’s law!

  3. Ekene paul

    Current cannot flow without voltage. True or false. Give reasons for your answer.

    • cormac

      Interesting question. In general, yes – current flows as a result of an energy difference (voltage). If there is no energy source, i.e. energy differential to push it, there is no reason for current to flow.
      You may be thinking of superconductors, which in principle offer no resistance to current flow. However, you will still get zero current for zero voltage even in a superconductor.

  4. Njoku uchechukwu Gabriel

    Thank you and God bless you. Have a nice day.

  5. Yes, voltage is a representation of electric potential energy per unit charge. voitage is course while current is effect

  6. Udoh chigozie

    Does increase in voltage cuases increase or decrease in curent. Give reason for ur answer

    • cormac

      In most materials, an increase in voltage will cause an increase in current. This is because the voltage source provides the energy that drives the electrons around the circuit. the higher the voltage, the bigger the current.
      And if you reverse the voltage, the current will run in the opposite direction

  7. Roger Holden

    Imagine that just the power cord from the wall to an electric motor was somehow superconductive (not the motor itself). Ignoring the energy costs of cooling the powercord to the superconductive state, what are the implications for power savings? In this thought experiment, the motor can be redesigned to adapt and take advantage of any changes in the current/voltage input into the motor from the superconductive power cord.


    what is the relation between current an voltage for superconductors.if you apply v voltage across the L length superconducting cable then what will be the current?

    • cormac

      Good question. You might think I = V/R = infinite, but Ohm’s law does not apply – instead, once started, a current will flow with zero applied voltage – v useful!.

  9. Mastewal

    I need help immediately, i knw that in most materials v and I are linear. But can we Say that voltage is always directly proportional to current?? Jst like force is directly proportional to acceleration always.

  10. Mastewal

    2. Another thing is that we say that charge flows over a wire… Does really the elections move and we say that a current or is it only the energy that is moving????

  11. kdawg

    I am making magnetoresistance measurement with 4 probe measurement but I cant understand; how an applied current changes the V in another part of the sample. (my physic background is very bad)

  12. John

    @kdawg, what kind of magnetoresistance are you using, a simple magneto-resistor: ?

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