## Electrical Power

### In the previous sections of this unit, it has been shown that Energy can be changed from one form into another. Even though the Energy type changed, the total Energy of the system remained constant. This section will cover how quickly Energy is converted from one form into another.

### The rate of transfer of Energy is known as the Power. The units for Power are Watts (W) and the Power of a system can be found using the following formula:-

### P = ^{E }/ _{t}

### Where:-

### P = Power (W)

### E = Energy (J)

### t = Time (s)

## Example 1 -

### A light bulb has a Power rating of 100 W. If the light bulb is used for 10 minutes, what is the total Energy used by the bulb?

### P = E / t

### E = P x t

### E = 100 x ( 10 x 60 )

### E = 60000 J

### E = 60 kJ

## Power in Electrical Circuits

### When a current flows through an Electrical circuit, Energy is transferred from the battery to the components. In the components, this Electrical Energy is converted into other forms, such as heat or light. This flow of Energy around the circuit depends the Voltage and Current within the circuit:-

### 1. Increasing Current - Faster flow of Charge and therefore faster Energy flow.

### 2. Increasing Voltage - Each unit of Charge has more Energy and therefore more Energy flows through the circuit.

### This faster Energy flow means a higher rate of Energy flow - a larger Power.

### Power in an Electrical Circuit can be found using the following formula:-

### P = I x V

### Where:-

### P = Power (W)

### I = Current (A)

### V = Voltage (V)

## Example 2 -

### How much Power is used by an Iron if it draws a Current of 5.6 A from a Mains supply?

### P = I x V

### P = 5.6 x 230

### P = 1288 W

## Power and Ohm's Law

### By combining the above formula with Ohm's law (see Ohm's Law - Unit 2) it is possible to find two more formulae for Power :-

### P = I x V V = I x R

### By substituting Ohm's Law into the Power Formula, the following can be found :-

###

### P = I x ( I x R )

### P = I^{2} x R

### By Rearranging Ohm's Law to find I, then substituting into the Power formula, the following can be found :-

### P = ( V / R ) x V

### P = V^{2} / R

### The four Power Formulae can then be used to find Power in a range of Circuits :-

### P = ^{E}/_{t} P = I x V P = I^{2} x R P = V^{2}/R

### A Tropical Fish Tank has a Power Rating of 130W and is connected to Mains Electricity. Calculate the following :-

### 1. The Resistance of the Aquarium.

### 2. The Current flowing through the Aquarium.

### 3. The Total Energy used in 1 day.

### Resistance :-

### P = V^{2} / R

### R = V^{2} / P

### R = ( 230^{2} ) / 130

### R = 407 Î©

### Current :-

### P = I x V

### I = P / V

### I = 130/230

### I = 0.56 A

### Total Energy :-

### P = E / t

### E = P x t

### E = 130 x ( 1 x 24 x 60 x60 )

### E = 11232000 J

### E = 11.2 MJ

## Energy and Power in the Home

### The calculations above can be used to understand the amount of energy used in the home. However, as was seen in the Space unit, standard scientific units are sometimes too small to easily work with. As can be seen in example 3 above, the Joule is too small a unit to use this way. When dealing with energy use in the home, a new unit must be used, the kiloWatt-Hour (kWh). It is in this form that all electrical bills are calculated. 1 kWh of Energy is the amount of energy used by a 1 kilo-Watt device in one hour.

### 1 kWh = 3.6 MJ

### Note - The above conversion is found by calculating 1000J every second for 1 hour.

### The actual cost of using 1 kWh varies between suppliers or contracts, but on average the cost of using 1 kWh is approximately 16 pence. By finding the energy used in kWh, it is possible to find the cost of any device use.

## Example 4 -

### A kettle has a power rating of 1200 W and is used for 4 minutes. If 1 kWh costs 16p, what is the cost of boiling the kettle?

### 4 minutes = 4 / 60 hours = 0.067 hours

### Energy used by the kettle = 1.2 x 0.067

### Energy used by the kettle = 0.06 kWh

### Cost to boil kettle = 0.06 x 16

### Cost to boil kettle = 0.9 pence

## Mains Electricity

### The most common source of electrical Energy in the home is mains electricity. Mains electricity provides an alternating Current with a stated Voltage of 230 V, alternating at 50 Hz. This is accessed by using the appropriate plug type for that region. In the UK, the standard plug is a 3-Pin plug (type G) as shown below:-

### Note - There are 15 different types of plug in use across the World, each with different Voltage and Current limits. Just because an adaptor allows a plug to connect to a foreign socket does not mean it is safe to use - always check that the device is compatible with the country's mains values.

### The UK plug is designed with several important safety features, which can be seen in the diagram below :-

### Safety features of a 3-Pin plug:-

### 1. Plastic coated - Electrical insulator to prevent electrical shocks.

### 2. Earth wire - Connected to any exposed metal, conducts Current safely to Earth if there is a fault preventing Electrical Shocks (see below).

### Fuse - Breaks flow of Current if the Current becomes too high, prevent risk of overheating or fire (see below).

### 3. Cable grip - Holds flex (cable containing the three wires) in place to prevent wires being exposed.

## Fuses

### A fuse in a 3-Pin plug is a device used to prevent too high Current flow within a device. A fuse consists of a thin wire within a ceramic cartridge, as shown in the image below:-

### The fuse acts as simply a piece of wire, as long as the Current is at the operating value. If the Current is too high, the wire within the fuse melts, breaking the circuit. This prevents the device from overheating and possibly from starting a fire.

### Note - In everyday language, we say the fuse has 'blown'. Do not use the word 'blown' as this implies an explosion. The correct description is the fuse wire 'melts'.

### Fuses come in a range of values and every mains appliance will have a correct fuse to use. The correct fuse can be found by using information on the rating plate. The image below shows the rating plate of an electric drill:-

### The correct value of the fuse is not given, but can be found using one of the above power equations to calculate the operating Current. Once the operating Current is known, a fuse that has a slightly larger value should be used. A general rule for this is as follows:-

### 1. Under 720 W - use a 3 A Fuse.

### 2. Over 720 W - use a 13 A Fuse.

## The Earth Wire

### The Earth wire is an additional wire within the 3-Pin plug that, if the system is working correctly, does not carry any Current. The Earth wire's function is to provide a short, low Resistance path to 'Earth'.

### If a fault occurs by the Live wire coming into contact with the metal casing of a device, anyone touching that device will receive a dangerous electrical shock. This is because the person touching the casing will give the Current a path to 'Earth' through.

### The Earth wire works by providing a lower Resistance path which allows the current to flow easily to 'Earth'. This high Current flow causes the fuse to melt, breaking the circuit. This renders the device safe.