Electric Current, Potential Difference, and Ohm’s Law
Electric current is the rate of flow of charge, I = Q ÷ t, measured in amperes (A); potential difference (voltage) is the energy transferred per unit charge, V = W ÷ Q, measured in volts (V); and Ohm’s law states that for a conductor at constant temperature the current is proportional to the potential difference, V = IR, where R is the resistance in ohms (Ω). In brief: 1 A is 1 coulomb per second, 1 V is 1 joule per coulomb, and 1 Ω is 1 volt per ampere. A resistor that obeys Ohm’s law is called ohmic, and gives a straight-line V–I graph through the origin. Conventional current points from the positive terminal to the negative one, opposite to the flow of electrons.
Understanding current, voltage and resistance is the basis for all electric circuits. This guide defines the three quantities, states Ohm’s law and its limits, compares the quantities in a table, works through calculations and corrects common mistakes.
What is electric current?
Current is the flow of electric charge. In metals, the charge carriers are free electrons; in solutions, they are ions. I = Q ÷ t: if a charge Q passes a point in time t, the current is I. The unit, the ampere, is 1 C/s. Conventional current is defined as the flow of positive charge, from the positive terminal of the supply, around the circuit, to the negative terminal. The electrons actually drift the other way, and slowly: in a copper wire carrying a few amperes, the drift speed is typically less than a millimeter per second, but the electric field that sets them in motion spreads at nearly the speed of light, so the lamp lights immediately. Current is measured with an ammeter connected in series. In a series circuit, the same current flows through all components; at a junction, the total current entering equals that leaving (conservation of charge).
What is potential difference?
The potential difference (p.d.) between two points is the energy transferred per unit charge in moving between them: V = W ÷ Q. A 12 V battery gives 12 J of energy to each coulomb of charge that passes through it, and a lamp across 12 V converts 12 J of electrical energy per coulomb to light and heat. The electromotive force (emf) of a source is the energy given to each coulomb by the source. A voltmeter is connected in parallel across the component to measure the p.d. Water analogy: p.d. is like the pressure difference that drives water through a pipe, and current is the flow rate.
What is Ohm’s law?
Georg Ohm found that for metallic conductors at constant temperature, the current is proportional to the p.d.: V = IR. The resistance R = V ÷ I measures how much the component opposes current, in ohms. It depends on the material, length, cross-sectional area and temperature of the conductor. The law applies to ohmic conductors, such as metal wires and resistors at constant temperature; it does not apply to:
- filament lamps: the resistance rises as the filament heats up, so the V–I graph curves;
- diodes: conduct in one direction only (little current until a threshold voltage of about 0.6 V for silicon);
- thermistors and light-dependent resistors: the resistance changes with temperature and light.
Electrical quantities compared
| Quantity | Symbol | Unit | Definition | Measured with |
|---|---|---|---|---|
| Current | I | ampere (A) | Q ÷ t | Ammeter (series) |
| Potential difference | V | volt (V) | W ÷ Q | Voltmeter (parallel) |
| Resistance | R | ohm (Ω) | V ÷ I | Ohmmeter or V and I |
| Charge | Q | coulomb (C) | I × t | — |
Worked example: current, charge and resistance
- Charge. A current of 2.0 A flows for 60 s. Q = It = 2.0 × 60 = 120 C. The number of electrons is 120 ÷ 1.60 × 10−19 = 7.5 × 1020.
- Ohm’s law. A resistor of 6.0 Ω is connected to a 12 V supply. I = V ÷ R = 12 ÷ 6.0 = 2.0 A.
- Finding the resistance. A lamp has a p.d. of 6.0 V across it and a current of 0.50 A. R = 6.0 ÷ 0.50 = 12 Ω.
- Energy. The charge of 120 C from item 1 passes through the 12 V supply: W = QV = 120 × 12 = 1,440 J.
- From a graph. A V–I graph for a resistor passes through (0.10 A, 0.50 V) and (0.40 A, 2.0 V). The gradient is V ÷ I = 0.50 ÷ 0.10 = 5.0 Ω (and 2.0 ÷ 0.40 = 5.0 Ω), a straight line through the origin, so the resistor is ohmic with R = 5.0 Ω.
How were these laws discovered?
Alessandro Volta invented the battery in 1800. André-Marie Ampère studied the forces between currents in the 1820s, and the unit is named in his honor. Georg Simon Ohm published his law in 1827 after experiments with wires of different lengths, though it was not accepted at first. The ohm was adopted as the unit in 1881, and the 2019 SI redefinition fixed the ampere by the value of the elementary charge.
Which mistakes are common?
Mistake 1: Saying that current is used up in a lamp
The current is the same on both sides of a component in a series circuit. Energy is transferred, not current.
Mistake 2: Connecting a voltmeter in series
Voltmeters are connected in parallel with the component, and ammeters in series.
Mistake 3: Applying V = IR to all components
For non-ohmic devices, R = V ÷ I still gives the resistance at that point, but it is not constant.
Mistake 4: Confusing the direction of conventional current and electron flow
They are opposite in metals.