Electric Potential Difference

Electric potential difference — commonly called voltage — is one of the most fundamental ideas in circuit electricity. It describes the work done per unit positive charge when a charge moves between two points in an electric field. Think of it like the difference in height between two points on a hillside: a ball naturally rolls downhill because there is a gravitational potential difference. Similarly, positive charges 'roll' from a region of higher electric potential to a region of lower electric potential, and this movement constitutes an electric current. Without a potential difference, charges have no net driving force and no current flows. The concept is closely tied to energy. When a battery is said to have a voltage of 9 V, it means the battery does 9 joules of work on every single coulomb of charge it pushes around the circuit. That energy is then transferred to components — resistors, bulbs, motors — which convert electrical energy into heat, light, or mechanical energy. Potential difference is therefore the mechanism by which a source of electrical energy communicates 'how much energy per charge' is available to the rest of the circuit, making it the key quantity that governs how much power any component can receive. It is important to distinguish electric potential difference from electric potential itself. Electric potential at a single point is defined relative to an arbitrary reference (often 'earth' or infinity), whereas potential difference is always measured between two specific points and has an unambiguous, physically meaningful value. In circuit analysis, we almost exclusively work with potential differences rather than absolute potentials.

Key takeaways
  • Work and charge — the core idea
  • The unit: the volt
  • Direction and sign convention
  • Measuring potential difference
  • Potential difference across series and parallel components

Work and charge — the core idea

Whenever a charge moves through an electric field, the field does work on it (or work is done against it). The electric potential difference between two points A and B is defined as the work done by an external force in moving a unit positive charge from A to B, without acceleration, divided by the magnitude of that charge. This is analogous to the way gravitational potential energy per unit mass defines gravitational potential. The key word is 'per unit charge': a larger charge would require proportionally more work, so dividing by the charge gives a quantity that describes the field itself, not the particular charge used to probe it.

The unit: the volt

The SI unit of potential difference is the volt (V), named after Alessandro Volta. One volt is defined as one joule of work done per one coulomb of charge: 1 V = 1 J C⁻¹. This definition immediately tells you how to think about voltage: a 230 V mains supply does 230 J of work on each coulomb of charge that passes through it. A 1.5 V cell does 1.5 J per coulomb — a much gentler push. The volt is also expressible as 1 V = 1 kg m² s⁻³ A⁻¹ in base SI units, though in practice 'joules per coulomb' is the most useful form.

Direction and sign convention

Potential difference is a signed quantity. If the potential at point A is higher than at point B, then V_AB = V_A − V_B is positive, and a positive charge released between those points would naturally move from A to B (losing potential energy, gaining kinetic energy). If V_AB is negative, the field opposes motion from A to B. In circuit diagrams, the conventional current flows from the positive terminal (higher potential) of a battery to the negative terminal (lower potential), and each component experiences a 'voltage drop' equal to the energy dissipated per unit charge as current passes through it.

Measuring potential difference

Potential difference is measured using a voltmeter, which is always connected in parallel across the component of interest. An ideal voltmeter has infinite resistance so it draws no current and does not disturb the circuit. In practice, voltmeters have very high (but finite) resistance. The reading gives the energy transferred per coulomb between the two terminals of the component. This is distinct from an ammeter, which measures current and must be placed in series. Remembering this placement rule — voltmeter in parallel, ammeter in series — is essential for circuit experiments.

Potential difference across series and parallel components

In a series circuit, the total potential difference of the supply equals the sum of the potential differences across each component (Kirchhoff's Voltage Law). This is a conservation-of-energy statement: all the energy given to each coulomb by the battery is fully accounted for by the drops across each resistor. In a parallel circuit, each branch has the same potential difference across it — they all connect between the same two nodes. Understanding these rules is the gateway to analysing any complex circuit systematically.

The Key Equation

V=WQV = \frac{W}{Q}
  • V — Electric potential difference (Volt (V)): The energy transferred per unit charge between two points; measured in joules per coulomb.
  • W — Work done (energy transferred) (Joule (J)): The total electrical energy transferred when charge Q moves between the two points.
  • Q — Electric charge (Coulomb (C)): The quantity of electric charge that moves between the two points.

Worked Example

Problem. A battery moves 4.0 C of charge around a circuit and does 48 J of work on the charge. (a) Calculate the potential difference (e.m.f.) of the battery. (b) If 20 J of that energy is dissipated across a resistor R₁, what is the potential difference across R₁?

Vbattery=12 V,VR1=5.0 VV_{\text{battery}} = 12\text{ V},\quad V_{R_1} = 5.0\text{ V}

Answer. Battery e.m.f. = 12 V; potential difference across R₁ = 5.0 V

Figure
Diagram
Electric Potential Difference in a Simple Circuit+−12 VR₁5 V dropR₂7 V dropVHigh potential (+12 V)Low potential (0 V)I →V = W/Q: each component drops potential proportional to energy dissipated per coulomb
Origins · 1 minAlessandro Volta and how this was discovered
AV
Alessandro Volta
1745–1827 · Italian

Alessandro Volta invented the voltaic pile in 1800 — the world's first electrochemical battery — which was the first device capable of producing a sustained, steady electric potential difference. By stacking alternating discs of zinc and copper separated by brine-soaked cloth, Volta demonstrated that a continuous voltage could drive a persistent electric current. His work gave scientists, for the first time, a controllable source of electrical potential difference to experiment with, directly enabling the entire field of circuit electricity. The volt, the SI unit of potential difference, is named in his honour. Volta was so sceptical of Luigi Galvani's 'animal electricity' theory that his attempts to disprove it accidentally led him to invent the battery — one of history's most productive scientific disagreements.

  • Electric Current — Current is the flow of charge driven by a potential difference; the two quantities are inseparable in circuit analysis.
  • Resistance and Ohm's Law — Ohm's Law (V = IR) directly relates potential difference, current, and resistance, making it the core equation of circuit analysis.
  • Electromotive Force (e.m.f.) — E.m.f. is the potential difference supplied by a source of electrical energy; understanding the distinction between e.m.f. and terminal voltage builds directly on potential difference.
  • Electrical Power and Energy — Electrical power (P = IV) combines potential difference and current, linking voltage directly to the rate of energy transfer in a circuit.