Ohm's Law - Electricity and Electronic Circuits Step by Step

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.

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.

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\ \text{V}, \quad R = 4\ \text{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 = \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.

\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}

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.

\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}

Substitute the voltage and the resistance

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

I = \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 = \frac{V}{R} = \hl{3}\ \text{A}