Energy and power in circuits

In a nutshell

Electrical devices are built to transfer energy. The power in a circuit is the rate at which this energy transfer occurs.

Equations

Word equation	Symbol equation
$energy \space transferred = charge \times potential \space difference$	$E = Q \times V$
$power = \frac{energy \space transferred}{time}$	$P = \frac{E}{t}$
$power = current \times potential \space difference$	$P = I \times V$
$power = (current)^2\times resistance$	$P = I^2 \times R$

Variable definitions

Quantity name	symbol	unit name	unit
$energy \space transferred$	$E$	$joule$	$J$
$power$	$P$	$watt$	$W$
$current$	$I$	$ampere$	$I$
$potential \space difference$	$V$	$volt$	$V$
$charge$	$Q$	$coulomb$	$C$
$resistance$	$R$	$ohm$	$\Omega$
$time$	$t$	$second$	$s$

Energy in circuits

When an electrical charge goes through a change in potential difference, work is done against resistance and energy is transferred.

Energy is supplied to the charge at the power source. The charge then transfers this energy when it goes through a potential drop in components elsewhere in the circuit.

Electrical appliances

Electrical appliances are designed to transfer energy to components in the circuit when a current flows.

Example

Kettles transfer electrical energy from the mains supply to the thermal energy store of the heating element inside the kettle.

Note: No appliance transfers all the energy with perfect efficiency. The larger the current, the more energy is transferred to the thermal energy stores of the components, which increases their resistance.

Heating in circuits

Heating up a component will generally reduce its efficiency. Also, if the temperature gets too high, then this can cause components in the circuit to melt. This will cause the component to stop working, and may affect the performance of the circuit.

Fuses are safety devices for electronic circuits. They are designed to melt if the current becomes too high. This breaks the circuit and protects the high current from damaging the other components in the circuit.

There are some advantages of heating in circuits, such as with the example below.

Example

A toaster uses coils of wire with a very high resistance. When a current passes through these coils of wire, the temperature of the wire increases significantly, to the point where the wire glows and gives of infrared radiation. This radiation then transfers to the bread, which cooks it. Filament bulbs and electric heaters follow a similar operating principle.

Power in circuits

The total energy used by an appliance depends on how long it is activated for, and its power. The power of an appliance is the rate of its energy transfer (per second). The power of an appliance can be calculated with the following equation:

$power = \frac{energy \space transferred}{time}$

$P = \frac{E}{t}$

The power transferred by an appliance depends on the current flowing through it and the potential difference across it. The following equation can be used to calculate the power of an appliance:

$power = current \times potential \space difference$

$P = I \times V$

Combining the two equations above, the energy transferred by an electrical component can be found with the following equation:

$energy \space transferred = current \times potential \space difference \times time$

$E = I \times V \times t$

Example

A $1.5 \space kW$ hair dryer is connected to a $230 \space V$ mains supply. Find the current that is flowing through the hair dryer.

First, write out the quantities needed and make sure they are in the correct form:

$P = 1.5 \space kW = 1500 \space W$

$V = 230 \space V$

Next, write down the equation you need to use:

$P = I \times V$

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

Then, substitute the values into the equation:

$I = \frac{1500}{230}$ 

Don't forget to include your units:

$I = 6.5 \space A$

There is $\underline{6.52 \space A}$ of current flowing through the hair dryer when it is connected to the mains supply.

Energy transferred

The energy transferred by an appliance depends on the potential difference across it and the charge flowing through it. The equation for calculating the energy transferred by an appliance is:

$energy \space transferred = charge \times potential \space difference$

$E = Q \times V$

Example

An electric razor contains a $3\space V$ battery. $200 \space C$ of charge passes through the razor over the duration it is used. Calculate the energy transferred.

First, write out the quantities needed and make sure they are in the correct form:

$Q = 200 \space C$

$V = 3\space V$

Next, write down the equation you need to use:

$E = Q \times V$

Then, substitute the values into the equation:

$E = 200 \times 3$

Don't forget to include your units:

$600 \space J$

The electric razor transfers $\underline{600 \space J}$ of energy over the duration it is used.