The relationship between voltage, current and resistance
Ohm's law describes a simple, linear relationship between three quantities in an electrical circuit: voltage (V), current (I) and resistance (R). It states that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance, usually written as V = I × R. The relationship was published by German physicist Georg Simon Ohm in 1827 and remains the foundational equation of circuit analysis.
The three quantities have standard SI units: voltage is measured in volts (V), current in amperes (A), and resistance in ohms (Ω). Ohm's law applies precisely to 'ohmic' components — materials and devices whose resistance stays constant across the range of voltage and current being considered, such as a metal resistor at a stable temperature. Many real components are not ohmic: a filament light bulb's resistance rises as it heats up, and semiconductor devices such as diodes and transistors do not follow a straight-line voltage-current relationship at all.
Power: P = VI
Electrical power — the rate at which electrical energy is converted, for example into heat or light — follows directly from the same three quantities using the formula P = V × I, where P is power measured in watts (W). Substituting Ohm's law (V = I × R) into this power formula gives two additional, equivalent forms: P = I² × R and P = V² ÷ R, each useful depending on which two quantities are already known.
These three power formulas always agree for the same circuit, since they are algebraic rearrangements of the same underlying relationship rather than independent facts. Choosing which form to use is simply a matter of which two quantities — voltage and current, current and resistance, or voltage and resistance — are already available for a given calculation.
Worked example: solving a simple circuit
Consider a 9-volt battery connected across a 3-ohm resistor. Applying Ohm's law, the current flowing through the resistor is I = V ÷ R = 9 ÷ 3 = 3 amperes. The power dissipated by the resistor is then P = V × I = 9 × 3 = 27 watts.
This result can be checked using the alternative power formulas: P = I² × R = 3² × 3 = 9 × 3 = 27 watts, and P = V² ÷ R = 9² ÷ 3 = 81 ÷ 3 = 27 watts. All three forms agree, confirming the calculation, which is a useful check when working through a circuit problem by hand.
| Known quantities | Formula | Result |
|---|---|---|
| V = 9 V, R = 3 Ω | I = V ÷ R | 3 A |
| V = 9 V, I = 3 A | P = V × I | 27 W |
| I = 3 A, R = 3 Ω | P = I² × R | 27 W |
| V = 9 V, R = 3 Ω | P = V² ÷ R | 27 W |
Solving for any one variable
Ohm's law and the power formula together relate four quantities — voltage, current, resistance and power — and knowing any two of them is enough to find the other two through algebraic rearrangement. To find resistance from voltage and current, rearrange V = I × R to R = V ÷ I; applying this to the worked example above, R = 9 ÷ 3 = 3 Ω, confirming the resistor value used.
To find current from power and voltage, rearrange P = V × I to I = P ÷ V; using the example's power and voltage, I = 27 ÷ 9 = 3 A, again matching the original current. This flexibility — being able to solve for whichever quantity is unknown, from any pair of the other three basic quantities — is why Ohm's law and its rearranged forms are sometimes summarized together as an 'Ohm's law wheel' of related formulas.
A household safety note
Ohm's law is a precise mathematical relationship, but applying it to real household wiring involves practical factors beyond the formula itself: conductor resistance changes with temperature, components have manufacturing tolerances, and mains electricity carries a serious risk of injury or fire if handled incorrectly. The calculations in this guide are intended for education and estimation, not as authorization to open, modify or work on a live electrical installation.
Any work on household wiring, circuits or fixed electrical installations should be carried out or verified by a qualified, licensed electrician in accordance with local electrical codes. This applies even when a calculation like the one above seems straightforward, since real circuits also involve protective devices, wire gauge and ampacity ratings, and code-specific requirements that a simple Ohm's law calculation does not address.
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What is the formula for Ohm's law?
Ohm's law is V = I × R, where voltage (V, in volts) equals current (I, in amperes) multiplied by resistance (R, in ohms). It can be rearranged to solve for any of the three quantities: I = V ÷ R, or R = V ÷ I, depending on which two values are already known.
How do I calculate power using Ohm's law?
Power is calculated as P = V × I, in watts. Because V = I × R, this can also be written as P = I² × R or P = V² ÷ R, giving three equivalent ways to calculate power depending on which two quantities — voltage, current or resistance — are known. For example, 9 V across 3 Ω gives 3 A and 27 W using any of the three forms.
How do I find resistance if I know voltage and current?
Rearrange Ohm's law to R = V ÷ I. For example, a 9 V supply driving 3 A of current through a component implies a resistance of 9 ÷ 3 = 3 ohms. This rearrangement works for any pair of known voltage and current values.
Does Ohm's law apply to every electrical component?
No. Ohm's law applies exactly only to 'ohmic' components, whose resistance stays constant across the voltage and current range considered, such as a standard resistor at stable temperature. Non-ohmic devices, including filament light bulbs, diodes and transistors, do not follow this straight-line voltage-current relationship.
Is it safe to use Ohm's law calculations for home wiring projects?
Ohm's law calculations are useful for understanding and estimating circuit behavior, but they are not a substitute for qualified electrical work. Any household wiring, circuit or fixed installation work should be carried out or verified by a qualified, licensed electrician in accordance with local electrical codes.
Kaynaklar
- Ohm GS. Die galvanische Kette, mathematisch bearbeitet. Berlin, 1827 — original statement of Ohm's law.
- Bureau International des Poids et Mesures (BIPM). The International System of Units (SI Brochure), 9th edition, 2019 — definitions of the volt, ampere, ohm and watt.
- Horowitz P, Hill W. The Art of Electronics, 3rd edition, Cambridge University Press, 2015 — Ohm's law and non-ohmic devices.