Resistance and Ohm's Law

In a nutshell

Resistance is a measure of the opposition of current flow. Ohm's law states that the current is directly proportional to the potential difference between two points in a conductor given a constant temperature. As temperature increases resistance also increases.

Equations

Description	equation
Resistance	$R=\dfrac{V}{I}$

Variable definitions

quantity name	symbol	derived units	alternate units	si base units
$resistance$	$R$	$\Omega$	$V\ A^{-1}$	$kg\ m^2\ s^{-3}\ A^{-2}$
$potential\ difference$	$V$	$V$	$J\ C^{-1}$	$kg\ m^2 \ s^{-3}\ A^{-1}$
$current$	$I$	$A$		$A$

Resistance

Every component has a property known as resistance. This is a measure of the opposition of current flow or in other words it measures how hard it is for current to pass through a component. Resistors are components that have a known resistance and can be used to regulate current in circuits.

Resistance is symbolised by the letter $R$ and is measured in ohms, represented by the greek letter $\Omega$ . You can calculate it with the following equation:

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

Ohm's law

The equation above also represents Ohm's law. This law states that between two points in a conductor the current is directly proportional to the potential difference ( $I \propto V$ ) given a constant temperature, which means that when $I$ increases so does $V$ and vice versa. You can see this more clearly by rearranging the equation to make $V$ or $I$ the subject:

$\begin{aligned}V&=IR\end{aligned}$

$\begin{aligned}\\I&=\dfrac{V}{R}\end{aligned}$

Example

A resistor has a current of $5\ A$ flowing through it and a potential difference of $20\ V$ across it. What is the resistance of the resistor?

Firstly, write down all the known values:

$\begin{aligned}I&=5\ A \\V&=20\ V\end{aligned}$ 

Next, write down the equation for resistance:

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

Substitute all the values into the equation and calculate the resistance:

$R=\dfrac{20}{5}=4\ \Omega$

The resistor has a resistance of $\underline{4\ \Omega}$ .

Finding the resistance of a component

To measure the resistance of a component you can set up a standard test circuit. Firstly you need to connect wires and components as follows:

Physics; Electrical circuits; KS5 Year 12; Resistance and Ohm's Law

1.	Power source
2.	Variable resistor
3.	Test component
4.	Ammeter
5.	Voltmeter

component	Description
Power source	A cell or battery to power the circuit.
Variable resistor	To change the current through the circuit. If the resistance value is increased, this will reduce the current that is able to flow through the circuit, and vice versa.
Test component	The component to be tested (a fixed resistor in this case).
Ammeter	Connected in series anywhere in the circuit, to measure the current.
Voltmeter	Connected in parallel across the component to be tested, to measure the voltage.

Using the variable resistor to change the current of the circuit, measure the voltage across the resistor (or any component you want to test) at continuous intervals of $I$ . You can then plot a graph of $V$ against $I$ and end up with a graph that looks like the following:

Physics; Electrical circuits; KS5 Year 12; Resistance and Ohm's Law

Finally, calculate the gradient of the graph to find the resistance of the component.

Resistance and temperature

When you increase the temperature of a component all the positive ions and electrons inside it gain more energy and start to vibrate. This makes it harder for electrons to move through the material as they have an increased chance of colliding with an ion and therefore the resistance of the component increases.

Current flowing through a material makes it hotter which means that its resistance will increase and subsequently decrease the current.

Physics; Electrical circuits; KS5 Year 12; Resistance and Ohm's Law

This property is possessed by all components but a component that enhances it is the thermistor. This is a type of resistor whose resistance is highly dependent on temperature.

There are two types of thermistors; NTC (negative temperature coefficient) thermistors that show a decrease in resistance with increasing temperature and PTC(positive temperature coefficient) thermistors that show an increase in resistance with increasing temperature.

Exam tip: when dealing with thermistors at this level always assume you are working with NTCs!