Resistance and V = IR

By the end of this lesson

By the end you can define resistance as the potential difference across a component divided by the current through it, state its unit, and use $V = IR$ in all three rearrangements to find the resistance, the potential difference or the current.

What resistance actually measures

Push the same potential difference across a short thick copper wire and across a long thin filament, and very different currents flow. The wire lets charge through easily; the filament holds it back. Resistance is the quantity that measures that opposition.

For any component we measure two things at the same time:

the potential difference $V$ across it (in volts),
the current $I$ through it (in amperes).

Resistance is the ratio of those two measurements. A component with a large resistance needs a large potential difference to drive even a small current through it.

This is why resistance is measured in a unit built from volts and amperes rather than being a "basic" unit like the metre or the second.

Definition

Resistance

The resistance $R$ of a component is the potential difference $V$ across it divided by the current $I$ through it:

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

The unit is the ohm ( $\Omega$ ), where $1\ \Omega = 1\ \text{V A}^{-1}$ : one ohm is the resistance of a component that carries one ampere when one volt is across it.

Worked example: Finding a resistance from a voltmeter and an ammeter

A resistor has a potential difference of $6.0\ \text{V}$ across it and carries a current of $0.25\ \text{A}$ . Calculate its resistance.

Have a go first?

Quick check

Multiple choiceQuestion 1 · Recall

DefinitionQuestion 2 · Recall

Answer the 2 questions above to continue.