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 devices-appliance 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 devices-appliances 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 infra-structure 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.

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 kilowatt-hours (kWh).

      • 1 kilowatt-hour = 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 kilowatt-hour 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 kilowatt-hours and joules.

    • E is energy transferred in kilowatt-hours, 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:

      • E is energy transferred in joules, J

      • P is power in watts, W

      • t is time in seconds, s

    • 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).

      • Using the formula triangle: P = E/t and t = E/P

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

      • Using the formula triangle: P = E/t and t = E/P

  • d) Be able to calculate the cost of using mains electricity given the cost per kilowatt-hour.

    • 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

      • cost (p) = power (kW) x time (hours) x electricity unit cost (p/unit)

    • 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?

        • power 2.5 kW, time = 30/60 = 0.5 hour

        • units = 2.5 x 0.5

        • cost = 2.5 x 0.5 x 12 = 15p

      • (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?

        • cost (p) = power (kW) x time (hours) x electricity unit cost (p/unit)

        • power = 500/1000 = 0.5 kW

        • rearranging the equation

          • time = cost / (power x unit cost)

          • time = 20 / (0.5 x 12) = 20 / 6 = 3.33 hours (3 hours 20 minutes)

  • Check out your practical work you did or teacher demonstrations you observed, all of this is part of good revision for your module examination context questions and helps with 'how science works'.

    • reading the electricity meter at home on a daily or weekly basis where you may have looked for trends in usage and try to explain these, eg in terms of weather conditions - extra usage of heating systems in cold weather,

    • plan and carry out an investigation using an electrical joulemeter to measure the energy transferred by low voltage bulbs of different powers, low voltage motors and low voltage immersion heaters.

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