Ohm's Law

Ohm's Law

current = voltage / resistance

Ohm's law pins down the exact current a given voltage pushes through a given resistance: I = V/R. Twelve volts across four ohm gives three amperes.

Example

Ohm's law pins down the exact current a given voltage pushes through a given resistance: I = V/R. Twelve volts across four ohm gives three amperes. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A battery pushes current through a resistor

Here is a battery pushing current through a resistor, with an ammeter in the loop to read the current. The battery supplies 12 volts and the resistor is 4 ohm. What current flows?

V=12 V,R=4 ohmV = 12\ \text{V}, \quad R = 4\ \text{ohm}
A battery, a resistor, and an ammeterA single loop where a battery pushes current through a resistor and the ammeter reads the current.12 VA4 ohm

Ohm's law: current is voltage over resistance

Ohm's law says the current is the voltage divided by the resistance. The units agree: a volt per ohm is exactly an ampere.

I=VR(volt per ohm=ampere)I = \frac{V}{R} \quad (\text{volt per ohm} = \text{ampere})

With resistance fixed, voltage sets the current

Keep the resistor at 4 ohm. Raising the battery voltage raises the numerator of the fraction, so the current rises row by row.

VRI4 V4 ohm1 A8 V4 ohm2 A12 V4 ohm3 A\begin{array}{c|c|c}V & R & I \\4\ \text{V} & 4\ \text{ohm} & 1\ \text{A} \\8\ \text{V} & 4\ \text{ohm} & 2\ \text{A} \\12\ \text{V} & 4\ \text{ohm} & 3\ \text{A}\end{array}
Same resistor, different battery voltagesA single loop using the same resistor while the table compares three battery voltages and their currents.12 VA3 A4 ohm3 A

With voltage fixed, resistance sets the current

Now keep the battery at 12 volts. Raising the resistance raises the denominator of the fraction, so the current falls row by row.

VRI12 V3 ohm4 A12 V4 ohm3 A12 V6 ohm2 A\begin{array}{c|c|c}V & R & I \\12\ \text{V} & 3\ \text{ohm} & 4\ \text{A} \\12\ \text{V} & 4\ \text{ohm} & 3\ \text{A} \\12\ \text{V} & 6\ \text{ohm} & 2\ \text{A}\end{array}
Same battery, different resistorsA single loop using the same battery while the table compares three resistor values and their currents.12 VA3 A4 ohm3 A

Substitute the voltage and the resistance

Put in the battery's 12 volts and the resistor's 4 ohm.

I=12 V4 ohmI = \frac{12\ \text{V}}{4\ \text{ohm}}

Compute the current

Dividing gives a current of 3 amperes. The ammeter reads 3 amperes and the current arrow agrees: voltage, resistance, and current all match one rule.

I=VR=3 AI = \frac{V}{R} = \hl{3}\ \text{A}
The current through the resistorThe same loop now showing the current value that the ammeter reads and the arrow marks.12 VA3 A4 ohm3 A
electricity The flagship rule of circuits: with 12 V across 4 ohm the current is exactly 3 A, and the battery, resistor, and ammeter values all agree with I = V/R.