How Ohm's Law Works: Voltage, Current and Resistance

Ohm's law is the first equation most people meet in electronics, and it still governs almost every circuit built today. It links three quantities: voltage, current and resistance. Once you know two of them, the third follows directly. That simple relationship lets you size a resistor for an LED, predict how hot a heater wire will run, or check whether a sensor circuit is healthy.

This post defines each quantity, explains the law and its limits, shows how resistors combine in series and parallel, and works through a complete example. The aim is to make the equation feel like a description of what electric charge is doing inside a wire.

The three quantities

Voltage, measured in volts (V), is the energy per unit charge that drives charges through a circuit. A 9 V battery gives each coulomb of charge 9 joules of energy. Voltage is always a difference between two points, so you measure it across a component.

Current, measured in amperes (A), is the rate at which charge flows past a point. One ampere equals one coulomb per second. Current is the same everywhere along a simple series loop, because charge cannot pile up at one point.

Resistance, measured in ohms (Ω), is how strongly a material opposes that flow. Resistance turns some electrical energy into heat as charges collide with atoms in the material. A resistance of 1 Ω means one volt pushes one ampere through the component.

The law itself

Ohm's law states that for many materials, at constant temperature, the current through a conductor is proportional to the voltage across it:

V = I × R

Rearranged, I = V / R and R = V / I. Doubling the voltage doubles the current when resistance is fixed. Doubling the resistance halves the current when voltage is fixed.

Ohm's law is an empirical rule, not a law of nature in the same sense as conservation of energy. It holds for metals at fixed temperature over a wide range of currents. Devices that break the rule are called non-ohmic. A diode conducts strongly in one direction and barely at all in the other, and a filament lamp's resistance rises as it heats up, so its current does not increase in a straight line with voltage.

Power, the companion formula

Electrical power, measured in watts (W), is the rate at which energy is converted. It is P = V × I. Substituting Ohm's law gives two more forms: P = I² R and P = V² / R. These show why a thin wire with high current gets hot. Heat grows with the square of current, so halving the current cuts heating to a quarter.

Series and parallel resistors

When resistors are connected in series, they share the same current and their resistances add:

R_total = R₁ + R₂ + R₃ + ...

When they are connected in parallel, they share the same voltage and the reciprocals add:

1 / R_total = 1/R₁ + 1/R₂ + 1/R₃ + ...

Parallel combinations always give a total resistance smaller than the smallest individual resistor. That is why adding a second wire to a path lowers the overall resistance and increases the total current a source can deliver.

The table below shows two example pairs of resistors.

Pair	Series total	Parallel total
2 Ω and 3 Ω	5 Ω	1.2 Ω
6 Ω and 3 Ω	9 Ω	2 Ω
10 Ω and 10 Ω	20 Ω	5 Ω

Worked example

A 12 V battery drives a circuit with a 4 Ω heater and a 2 Ω resistor in series.

1. Total resistance: R = 4 + 2 = 6 Ω.
2. Current: I = V / R = 12 / 6 = 2 A.
3. Voltage across the heater: V = I × R = 2 × 4 = 8 V.
4. Power in the heater: P = I² R = 2² × 4 = 16 W.
5. Power in the 2 Ω resistor: P = 2² × 2 = 8 W.
6. Total power from the battery: P = 12 × 2 = 24 W, which equals 16 + 8.

The check at step 6 is worth doing every time. Power delivered by the source must equal power dissipated in the resistors, so the numbers must agree.

Resistivity and the shape of a wire

Resistance depends on material and geometry. For a uniform wire, R = ρ L / A, where ρ is resistivity, L is length and A is cross-sectional area. Longer wires have more resistance. Thicker wires have less. Resistivity is a property of the material itself.

The table below gives approximate room-temperature resistivities. The values vary with purity and temperature, so they should be treated as typical rather than exact.

Material	Resistivity (Ω·m, approx.)	Use
Silver	1.6 × 10⁻⁸	Best conductor, expensive
Copper	1.7 × 10⁻⁸	Household wiring
Aluminium	2.8 × 10⁻⁸	Power lines
Nichrome	1.1 × 10⁻⁶	Heating elements
Pure silicon	about 2.3 × 10³	Semiconductor devices
Glass	10¹⁰ to 10¹⁴	Insulation

Nichrome is used in toasters and space heaters because its resistivity is roughly 65 times that of copper, so it converts more energy into heat per unit length, and it resists oxidation at high temperature.

Why current does not get used up

Some people imagine that a resistor consumes current. It does not. The current entering a resistor equals the current leaving it. What changes is the energy carried by each charge. Charges gain energy from the source and lose it as heat in the resistor. The rate of charge flow stays the same along a series path.

Limits of the simple model

Ohm's law assumes constant temperature, steady current and a material whose resistance does not depend on the direction of the field. At very high frequencies, skin effect pushes current toward the surface of a conductor and changes the effective resistance. At very low temperatures, some materials become superconductors and their resistance drops to zero. In those cases the model needs refinement, but for everyday DC circuits with resistors and wires it is accurate enough to design with.

Key takeaways

Ohm's law, V = I R, links voltage, current and resistance for most conductors at fixed temperature. Series resistances add, parallel resistances combine through reciprocals, and power follows from P = I² R. Material and geometry set resistance through the resistivity formula. Checking that source power equals dissipated power is a quick way to catch arithmetic mistakes in any circuit calculation.