Ohm's Law: Voltage, Current and Resistance

What does V = IR mean?

In Ohm’s law, V is the voltage across an element, I is the current through it and R is its resistance. For an ohmic element at stable physical conditions, the voltage-current relationship is proportional: double the voltage and the current doubles.

The equation can be rearranged to find current, I = V ÷ R, or resistance, R = V ÷ I. Keep the units consistent: volts, amperes and ohms. The measured voltage and current must refer to the same element and operating condition.

The condition matters. A filament heats up and its resistance changes. A diode does not have the same proportional relationship across its operating range. A whole appliance can contain many components with different behavior.

Further reading: 9.4 Ohm's Law · 9.3 Resistivity and Resistance

Worked example: a fictional 12-volt circuit.

Place 12 V across an ideal 6 Ω resistor. Divide voltage by resistance: 12 ÷ 6 = 2 A. The resistor transfers 24 W of electrical power into heat in this model.

Hold the supply at 12 V and change the resistance to 12 Ω. Current becomes 1 A and power becomes 12 W. Higher resistance has reduced current because the voltage stayed fixed.

Use the learning tool below to change either value. It assumes a steady DC source and a fixed resistor. The result does not specify a practical component, wiring arrangement or safe installation.

Further reading: 9.4 Ohm's Law · 9.5 Electrical Energy and Power

Ask what stays fixed before predicting heat.

For a resistor, power can be expressed as I²R or V²/R. These expressions agree when V = IR. They describe different comparisons depending on what you hold constant.

At fixed current, a higher resistance dissipates more power. At fixed voltage across the resistor, a higher resistance draws less current and dissipates less power. “More resistance always means more heat” misses this distinction.

A deteriorating connection can concentrate heat in a small area while the rest of a circuit continues operating. Current, contact area, material condition and heat removal all matter. A full circuit can also change its behavior as a connection degrades; it is not automatically a fixed-current model.

Further reading: 9.5 Electrical Energy and Power

Resistance exists in conductors and connections.

Real conductors have resistance. For a uniform material at a given temperature, resistance increases with length and decreases with cross-sectional area. Material resistivity also matters. Conductor temperature can change the resistance.

This is why the entire current path matters in a simple voltage-drop example. A calculation using only one part of the loop can miss part of the resistance. AC analysis may also need reactance and the combined effect called impedance.

A resistance formula cannot tell you whether a particular existing termination is sound. A new smell, visible damage, unusual heat or intermittent operation deserves attention to the actual condition.

Further reading: 9.3 Resistivity and Resistance

Motors and electronics need a richer model.

An AC motor involves magnetic fields, mechanical loading and a voltage-current relationship that changes during starting and operation. Electronic equipment may actively regulate its input or draw current in pulses. Neither should automatically be modeled as one unchanged resistor.

Ohm’s law remains useful for parts of the analysis. The mistake is treating a simplified component example as a complete diagnosis or a universal equipment-sizing rule.

Further reading: 15.2 Simple AC Circuits · 15.4 Power in an AC Circuit · What is a nonlinear load?

Questions you may be asking.