The heating effect of current

In a nutshell

Electric current passing through a wire will cause the wire to heat up due to the current heating effect. Depending on the situation, the current heating effect can be either advantageous or dangerous.

Equations

Word equation	symbol equation
$power = (current)^2 \times resistance$	$P = I^2 \times R$

Variable definitions

quantity name	symbol	unit name	unit
$power$	$P$	$watt$	$W$
$current$	$I$	$ampere$	$A$
$resistance$	$R$	$ohm$	$\Omega$

Current heating effect

When an electric current passes through a wire, the wire warms up. This is because the electrons collide with the ions in the wire, passing their kinetic energy to the ions, causing them to vibrate more. These vibrations cause the temperature of the wire to increase.

Advantages and disadvantages

There are a number of situations where the current heating effect is useful and also a number of situations when it is not useful.

Advantages	Disadvantages
Room heaters and water heating coils make use of the conversion of electrical energy to heat energy.	A major disadvantage of the current heating effect is the wastage of energy during power transmission in overhead cables. To minimise the energy wastage, power is usually transmitted through overhead cables at high voltages and low currents.
Light bulbs also make use of the current heating effect. The filament of a light bulb is made of tungsten metal, which glows when heated by the current flowing through it, thus giving out light.	The current heating effect can also damage or reduce the life of the components within a circuit.
Electric fuses are rated at specific current values. When the current flowing through it exceeds the rated value, the resulting heat melts the fuse and breaks the circuit. This protects the rest of the circuit from potentially being damaged by an abnormally high current.	Additional cooling systems or heat sinks need to be added to electrical circuits in order to minimise the heating effect, which adds to the cost.

Power

Electrical power can be calculated using the following equation, provided that both the current and resistance are known:

$power = (current)^2 \times resistance$

$P = I^2 \times R$

This equation can also be used to find the power "losses", known as $I^2 R$ losses.

Example

For a wire of a given resistance, doubling the current will increase the wasted energy by a factor of four.

Since this energy is transferred to the thermal energy store of the wire, the temperature of the wire will also increase by a factor of four.