Potential difference

• The potential difference (voltage) between two points is the work done to move one coulomb of charge between them:

  V = W / Q

  W is in joule, Q in coulomb, V in volt, so 1 V = 1 J/C. Two points have a potential difference of one volt when one joule of work is needed to carry one coulomb from one point to the other.

• It follows that W = V Q = V I t: the energy delivered to a part of a circuit equals the voltage across it times the charge that passes through it.

• • Potential difference is measured by a voltmeter, which is always connected in parallel across the two points.
  • It must have a very large resistance so that it takes almost no current from the circuit.

Worked example 1.2. The work done in moving 8 C of charge between two terminals is 120 J. The potential difference is V = W / Q = 120 / 8 = 15 V. If instead a 6 V battery moves 25 C round a circuit, the energy it supplies is W = V Q = 6 × 25 = 150 J.