What Is Ohm's Law? V = I × R Explained Simply

The one equation that ties a circuit together

Ohm's law describes how three quantities in a circuit relate: voltage (V), the electrical pressure pushing charge; current (I), the rate of charge flow; and resistance (R), how much a component opposes that flow. The relationship is simply V = I × R. Double the voltage across a fixed resistance and the current doubles; double the resistance at fixed voltage and the current halves.

Named after the German physicist Georg Ohm, the law holds for ohmic materials — resistors, most metals, and heating elements — where resistance stays roughly constant across a range of voltages. It is the single most useful relationship in practical electronics, letting you predict a current from a known voltage and resistance, or size a resistor to set a target current.

The Ohm's law triangle

The triangle trick helps you rearrange the formula without algebra. Draw a triangle with V at the top, and I and R in the two bottom corners. Cover the quantity you want: cover V and you see I × R side by side (multiply); cover I and you see V over R (divide); cover R and you see V over I (divide). It works because V = I × R, I = V / R, and R = V / I are the same equation rewritten.

Keep your units consistent. Volts, amperes, and ohms combine directly. If a value is in milliamperes (mA) or kilohms (kΩ), convert first: 1 mA = 0.001 A and 1 kΩ = 1000 Ω. Mixing prefixes is the most common source of errors that are off by a factor of a thousand.

Worked examples and adding power

Example 1: a 9 V battery drives a current of 30 mA through a resistor. What is the resistance? R = V / I = 9 / 0.03 = 300 Ω. Example 2: what current flows when 5 V is applied across a 220 Ω resistor? I = V / R = 5 / 220 = 0.0227 A, about 23 mA. Example 3: the voltage across a 470 Ω resistor carrying 10 mA is V = I × R = 0.01 × 470 = 4.7 V.

Ohm's law pairs naturally with the power equation P = V × I, measured in watts (W). Combining the two gives P = I² × R and P = V² / R, handy for checking that a resistor is rated for the heat it will dissipate. In example 3, the resistor dissipates P = V × I = 4.7 × 0.01 = 0.047 W, so a standard 0.25 W resistor has ample margin.

Frequently asked questions

What are the three forms of Ohm's law?

V = I × R to find voltage, I = V / R to find current, and R = V / I to find resistance. All three are the same relationship rearranged for the unknown quantity.

Does Ohm's law work for AC circuits?

For purely resistive AC circuits, yes, using RMS values. When capacitors or inductors are present, resistance is replaced by impedance (Z), and the relationship becomes V = I × Z.

Why is my calculated current off by 1000?

Almost always a unit mismatch. Convert milliamperes to amperes (÷1000) and kilohms to ohms (×1000) before applying the formula, so every value is in base SI units.

Is every material ohmic?

No. Diodes, LEDs, transistors, and filament lamps are non-ohmic — their resistance changes with voltage or temperature, so V = I × R does not hold as a straight line. Ohm's law applies cleanly to fixed resistors and most metals at constant temperature.