The usefulness of electrical appliances, transferring electrical energy and cost
calculations
Doc Brown's Physics Revision
Notes
Suitable for GCSE/IGCSE Physics/Science courses or
their equivalent
This page will answer many questions e.g.
Why are electrical devices so useful?
How do we calculate the energy transferred
when an electrical appliance is in use?
What do we mean by a unit of electricity
used?
How do we calculate the cost of running an
electrical device?
The usefulness of electrical appliances

Appreciate that we often use electrical
appliances because they transfer energy into other useful at the flick of a switch ie very
convenient!

Just think of all the
devicesappliance that run off electricity in the home eg light bulbs, TV,
refrigerator, CD player, radio, oven, mobile phone charger, computers,
battery charger, Hoover, food mixer, microwave, iron, immersion heater,
telephone, internet etc. etc.!

Think of the importance of these
devicesappliances in your life  music/TV on demand, food safely stored in
the fridge, light to read by in the evening

Try to imagine life without your
domestic electricity and think how wonderful 240V is!

Quite simply the convenience and
usefulness of mains electricity to our way of life and standard of living is
incalculable, so don't waste it!

Know how to calculate how much energy
is transferred by an appliance and how much the appliance costs to run.

You should be able to use
their skills, knowledge and understanding to:

compare the advantages and
disadvantages of using different electrical appliances for a particular
application,

you will be required to compare
different electrical appliances, using data provided,

this may involve energy use and
cost effectiveness.

and consider the implications of instances when electricity is not
available.

For developing countries where
infrastructure lacks a reliable mains electricity supply, battery operated
devices can be used and even clockwork radios have been designed.

However, batteries are costly
despite being a convenient supply of stored chemical energy which converts
to electrical energy on demand. They also don't last very long!

In the case of a clockwork
powered radio, when the radio is 'wound up' the energy is stored as elastic
potential energy and again released as needed to listen to the radio, for
free! This completely avoids the need for costly batteries and their safe
disposal to avoid pollution.

Without mains electricity,
communities in developing countries cannot have the same standard of
material living.
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Electricity Cost Calculations

a) Know and appreciate examples of energy transfers
that everyday electrical appliances are designed to bring about.

b) Know that the amount of energy an
appliance transfers depends on how long the appliance is switched on and its
power.

The quantity of electricity that
is transferred ('used') in an appliance depends on its power and how long
you use it for ie time its switched on.

Energy is measured in joules (E
in J) and power in watts (P in W)

1 watt = 1 J of energy
transferred in 1 second (1 W = 1 J/s)

Since a joule is a very tiny
amount of energy, we often quote power in kilowatts (P in kW).

1 kW = 1000 W = 1 1000 J/s

A bulb might be quoted with a
50W rating (50 J/s), an iron might be quoted as having a 500W or 0.5kW power
rating (500 J/s, 0.5kJ/s) and a three bar electric fire might have a 3kW
power rating (3 kJ/s, 3000 J/s).

However when dealing with large
amounts of electrical energy its more convenient to think and calculate in
kilowatthours (kWh).

1 kilowatthour = the amount of
electrical energy that a 1 kW appliance uses in 1 hour.

In fact, in terms of the
electricity use in a house, the term unit on your electricity bill
means a kilowatt hour and the price will quoted as eg '9p per unit',
in other words you will pay 9p for every kilowatthour of electrical energy
you use.

c) Be able to calculate the amount
of energy transferred from domestic mains electricity using the formula:

energy transferred by device
= appliance power x time

E = P x t

You
will not be required to convert between kilowatthours and joules.

E is
energy transferred in kilowatthours, kWh

P is power in kilowatts,
kW (1 kW = 1000 J/s)

t is
time in hours, h

rearrangements: P = E/t
and t = E/P

Also be able to use this equation when:

The power formula triangle for the units of power in watts (W),
units of energy in joules (J) and units of time in
seconds (s).

The power formula triangle for the units of power in kilowatts (kW),
units of energy in kilowatthours (kWh) and units of time
in hours (h).

d) Be able to calculate the cost
of using mains electricity given the cost per kilowatthour.

You should know this includes
both the cost of using individual appliances and the interpretation of
electricity meter readings to calculate total cost over a period of time.

1 unit of electrical energy used
= 1 kilowatt hour (kWh)

(i) Units of electricity
used = power (kW) x time (hours)

(ii) Cost of electricity
used = units x cost per unit

For an individual
appliance/device, combining (i) and (ii) gives for example

Examples of cost calculations:

(for the sake of argument we'll
call the price of electricity 12p per unit)

(a) What is the cost per
week of using a 40W light bulb for 36 hours in a week?

power = 40/1000 = 0.04 kW, units
= kWh = 0.04 x 36

cost = 0.04 x 36 x 12 = 17.3p
(3 sig. figs.)

It doesn't seem a lot, but
throughout a house it soon adds up, so always switch unwanted lights!

(b) What is the cost of
doing a single wash in a machine rated at 2.5 kW if it takes 30 minutes to
complete the washing and spin drying cycle?

(c)(i) Ignoring the
standing charge, what is the quarterly bill cost to a household that uses
650 units of electrical energy in three months?

cost = 650 x 12 = 7800p
or £78

(c)(ii) If the family wants to
cut the cost of the quarterly bill to £60, what is the maximum number of
units of electrical energy they can use?

cost = units x unit cost, so
units = cost/unit

cost = £60/12p = 6000/12 =
500 units

(d) How long could you
run a 500 W plasma TV screen for 20p?
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