Ohms Law

Overview

Ohm's law describes the fundamental relationship between voltage, current, and resistance in an electrical circuit: the current through a conductor is directly proportional to the voltage across it and inversely proportional to the resistance.

This principle applies to linear (ohmic) conductors — most metals at constant temperature. Non-ohmic devices such as diodes and thermistors do not obey Ohm's law.

Key Formulas

Ohm's Law

$V = I \cdot R$

Power Dissipation

$P = V \cdot I = I^2 R = \frac{V^2}{R}$

Energy

$E = P \cdot t$

Variables

Common SI Prefixes in Electrical Work

Currents, voltages, and resistances in practical circuits often span many orders of magnitude. The most frequently used prefixes are listed below.

Ohm's Law Calculator

Power Calculator

Unit Converter

Interactive Nomograms

The original resistance and power nomogram images are represented below as interactive Ohm's Law datasets.

Equivalent Expressions

Ohm's law can be rearranged to solve for any one variable when the other two are known:

$V = I \cdot R \qquad I = \frac{V}{R} \qquad R = \frac{V}{I}$

Similarly, the three forms of the power equation allow you to calculate power from whichever pair of quantities you have:

$P = V \cdot I \qquad P = I^2 R \qquad P = \frac{V^2}{R}$

Practical Examples

Example 1 — Simple Circuit

A 12 V battery supplies power to an 18 Ω resistor:

$I = \frac{V}{R} = \frac{12}{18} = 0.667 \text{ A}$

Power dissipated: $P = \frac{V^2}{R} = \frac{144}{18} = 8 \text{ W}$.

Example 2 — Finding Resistance

A 1 A current flows through a 230 V circuit:

$R = \frac{V}{I} = \frac{230}{1} = 230 \; \Omega$

Example 3 — Using SI Prefixes

A 3.3 kΩ resistor must carry 20 mA. The required voltage is:

$V = R \cdot I = 3300 \times 0.020 = 66 \text{ V}$

Example 4 — Appliance Analysis

A 100 W light bulb on a 230 V supply draws:

$I = \frac{P}{V} = \frac{100}{230} \approx 0.435 \text{ A}$

$R = \frac{V^2}{P} = \frac{230^2}{100} = 529 \; \Omega$

Practical Examples Summary

Restored Original Source Tables

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Ohm's Law Source Formula Relationships

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Original Source Images

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ohms law

Engineering Notes

• Temperature dependence: Resistance of metallic conductors increases with temperature. Ohm's law assumes constant temperature; at high currents the resulting temperature rise changes resistance and can violate the linear assumption.
• AC circuits: The basic DC form $V = IR$ extends to AC using impedance $Z$ in place of $R$: $V = I Z$. Reactive components (capacitors, inductors) introduce phase shifts between voltage and current.
• Power ratings: Resistors are rated for maximum power dissipation. Exceeding this causes overheating and failure. Always verify that calculated power is below the component rating with appropriate safety margin.
• Measurement safety: When measuring current with a multimeter, break the circuit and place the ammeter in series. Never connect an ammeter across a voltage source — its near-zero internal resistance will draw destructive current.
• Prefix arithmetic: Work in base SI units (V, A, Ω, W) during calculation and convert prefixes at input/output. Mixing prefixes without conversion is a common source of error.

References

• Ohm's Law — Engineering ToolBox (original source)