Resistance and Ohm's Law

Resistance is the opposition to the flow of current in a circuit. It determines how much current flows for a given potential difference.

The equation (Ohm’s law)

$V = IR$

Symbol	Quantity	Unit
$V$	Potential difference	V
$I$	Current	A
$R$	Resistance	$\Omega$ (ohms)

1 ohm means a p.d. of 1 V drives a current of 1 A.

Ohmic conductors

An ohmic conductor obeys Ohm’s law: current is directly proportional to potential difference, provided temperature is constant. The I-V graph is a straight line through the origin.

Examples: metal wires at constant temperature, fixed resistors.

Worked example

A 6.0 V battery drives a current of 0.25 A through a resistor. Calculate the resistance.

$R = \frac{V}{I} = \frac{6.0}{0.25} = 24\text{ }\Omega$

Worked example: finding current

A 12 V supply is connected to a 48 $\Omega$ resistor. Find the current.

$I = \frac{V}{R} = \frac{12}{48} = 0.25\text{ A}$

Factors affecting resistance

Factor	Effect on resistance
Longer wire	Higher resistance
Thinner wire (smaller cross-section)	Higher resistance
Higher temperature (for metals)	Higher resistance
Material	Different materials have different resistivities

Common errors and how to correct them

Using the p.d. of the battery instead of the p.d. across the component. If the circuit has more than one component, use the p.d. across the specific component, not the total e.m.f.

Stating “Ohm’s law says V = IR.” Ohm’s law specifically states that current is proportional to p.d. at constant temperature. $V = IR$ is the defining equation for resistance and always applies; Ohm’s law is a statement about the proportionality.

How to apply this in an exam

State the equation, substitute values, and calculate. Always use the p.d. across the component in question. State units ($\Omega$).