Ohm’s Law

Ohm's Law is one of the most fundamental relationships in electrical physics, describing how voltage, current, and resistance interact in a conducting material. Stated simply: the current flowing through a conductor is directly proportional to the voltage applied across it, provided that temperature and other physical conditions remain constant. This clean, linear relationship makes Ohm's Law an indispensable tool for analysing and designing electrical circuits, from the simplest torch to complex electronic devices. Think of electrical current like water flowing through a pipe. The voltage is analogous to the water pressure pushing the flow, while resistance is like the narrowness or roughness of the pipe that opposes the flow. A higher pressure (voltage) drives more flow (current), whereas a narrower pipe (higher resistance) restricts it. This analogy captures the essence of Ohm's Law: double the voltage and you double the current; double the resistance and you halve the current. The relationship is perfectly linear for ohmic materials. Not all materials obey Ohm's Law under all conditions — devices such as diodes, thermistors, and light-dependent resistors are called non-ohmic because their resistance changes with voltage or temperature. For ohmic conductors, however, a graph of voltage against current is a straight line through the origin, and the gradient of that line equals the resistance. Understanding when Ohm's Law applies — and when it does not — is a critical skill in circuit analysis.

Key takeaways
  • What is Voltage (Potential Difference)?
  • What is Current?
  • What is Resistance?
  • The Linear Relationship
  • Rearranging the Equation

What is Voltage (Potential Difference)?

Voltage, or potential difference (V), is the energy transferred per unit charge between two points in a circuit. It is measured in volts (V). Voltage is the 'electrical pressure' that drives charge carriers through a conductor — without it, no net current flows. A 9 V battery, for example, provides 9 joules of energy for every coulomb of charge it moves around the circuit.

What is Current?

Electric current (I) is the rate of flow of electric charge past a given point, measured in amperes (A). One ampere equals one coulomb of charge passing per second. Conventional current is defined as flowing from the positive terminal to the negative terminal of a supply, which is opposite to the direction of actual electron movement. Current is measured using an ammeter connected in series with the component under test.

What is Resistance?

Resistance (R) quantifies how strongly a material opposes the flow of electric current, measured in ohms (Ω). It arises because conduction electrons collide with the fixed lattice ions of the material as they drift through. A higher resistance means more collisions, less current for the same voltage, and more energy dissipated as heat. Resistance depends on the material's resistivity, its length, and its cross-sectional area.

The Linear Relationship

Ohm's Law states that V = IR for ohmic conductors at constant temperature. This means if you plot V on the y-axis and I on the x-axis for an ohmic resistor, you get a straight line through the origin with gradient equal to R. If instead you plot I vs V, the gradient equals 1/R (the conductance). Any deviation from a straight line through the origin is a sign that the component is non-ohmic — its resistance is changing with conditions.

Rearranging the Equation

Ohm's Law can be rearranged to solve for any one of the three quantities if the other two are known: V = IR gives the voltage; I = V/R gives the current; R = V/I gives the resistance. A useful memory aid is the 'Ohm's triangle': place V at the top, I and R at the bottom. Cover the quantity you want — what remains gives the formula. This flexibility makes Ohm's Law the starting point for almost every circuit calculation.

The Key Equation

V=IRV = IR
  • V — Voltage (Potential Difference) (Volt (V)): The electrical potential difference across the component, representing energy transferred per coulomb of charge.
  • I — Current (Ampere (A)): The rate of flow of electric charge through the conductor, measured in coulombs per second.
  • R — Resistance (Ohm (Ω)): The opposition to the flow of current offered by the conductor; ratio of voltage to current at constant temperature.

Worked Example

Problem. A resistor is connected to a 12 V battery. A current of 0.40 A flows through the resistor. (a) Calculate the resistance of the resistor. (b) If the battery is replaced with a 9 V supply, what current flows through the same resistor?

R=30 Ω,I=0.30 AR = 30\,\Omega,\quad I = 0.30\,\text{A}

Answer. The resistance is 30 Ω; the current with the 9 V supply is 0.30 A.

Figure
Diagram
Ohm's Law: V–I Graph for Ohmic and Non-Ohmic ConductorsCurrent, I (A)Voltage, V (V)OhmicresistorΔIΔVgradient = RNon-ohmic(e.g. bulb)OStraight line through origin → constant RCurve → R changes with I (non-ohmic)
Origins · 1 minGeorg Simon Ohm and how this was discovered
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Georg Simon Ohm
1789–1854 · German

Georg Simon Ohm formulated what we now call Ohm's Law in his 1827 publication 'Die galvanische Kette, mathematisch bearbeitet' (The Galvanic Circuit Investigated Mathematically). Using hand-made equipment including thermoelectric cells and wires of different lengths and thicknesses, he experimentally established that current is proportional to voltage and derived the relationship V = IR. He also introduced the concept of electrical resistance as a measurable, quantifiable property of a conductor. Ohm's initial publication was met with ridicule by the German scientific establishment, who considered his mathematical approach to physics inappropriate. He lost his teaching position as a result. It was only after British and French scientists praised his work that he was finally awarded recognition — including the Royal Society's Copley Medal in 1841, and the naming of the unit of resistance (ohm, Ω) in his honour.

  • Electric Current and Charge — Ohm's Law involves current (I) directly; understanding charge flow and the definition of the ampere is essential before applying V = IR.
  • Potential Difference and EMF — Voltage (V) is one of the three quantities in Ohm's Law; distinguishing between potential difference across a component and the EMF of a source is critical for circuit analysis.
  • Resistors in Series and Parallel — Ohm's Law is applied repeatedly to individual components when analysing series and parallel circuits, making it the foundation for all multi-resistor problems.
  • Electrical Power and Energy — The power dissipated in a resistor (P = IV = I²R = V²/R) is derived directly from Ohm's Law combined with the definition of power.