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

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

• 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 i.e. 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 = 1000 J/s

  • A bulb might be quoted with a 50W rating (50 J/s), an iron might be quoted as having a 500 W or 0.5 kW 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.

• Three formulae for calculating power, energy transferred and other things too!

  • If unsure about units of potential difference (p.d. in V), current in amperes (amps, A) or resistance in ohms (Ω) then read the first section of Ohm's Law and calculations using V = IR

  • 1.6A power P (W) = current I (A) x potential difference V (V)

    • P = IV

    • P in W or J/s,  I in amps A, V p.d. in volts.

    • The more energy transferred in a given time, the greater the power of the device.

    • The p.d. V tells you how much energy each unit of electrical charge transfers (V = E/Q, J/C.

    • See Electricity Part  3 for E = QV calculations).

    • The current I tells you how much charge passes a given point in a circuit per unit time (coulombs/second, C/s).

    • This means both p.d. and current affect the rate at which energy is transferred to an appliance from the electrical energy store to another energy store.

    • Examples of calculations using P = IV

    • It is better to be able to rearrange a formula rather than using a triangle

    • AQ1 A 2 kW electric fire is connected to a 240 V supply.

      • Calculate the current flowing through the electric fire.

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    • AQ2 The current flowing through an electric motor is 12 A.

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    • AQ3 What p.d. must a power supply have, to produce a power output of 2.0 kW from a machine through which 12.0 A flows?

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    • AQ4 A p.d. of 12.0 V is applied across the resistor of a device with a power of 8.0 W.

      • (a) Calculate the current flowing through the device.

      • (b) Calculate the resistance of the device.

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      • ANSWERS to AQ QUESTIONS at the end of the page

  • 1.6B power = current² x resistance

    • P = IV and since V = IR, substituting for V gives P = I²R

    • P = I²R

    • P in W or J/s,  I in amps A and p.d. in volts V, R in ohms Ω.

    • (this is useful if you don't know the p.d., but, you must know the resistance instead)

    • Examples of calculations using P = I²R

    • It is better to be able to rearrange a formula rather than using a triangle

    • BQ1 A current of 20 A passes through a resistance of 10 Ω.

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    • BQ2 A 2.0 kW electric fire has 4.0 A running through this heating appliance.

      • Calculate the resistance of the heating element.

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    • BQ3 A 20 Ω electrical device transfers energy with a power of 500 W.

      • Calculate the current flowing through the device.

      • -ANSWERS to BQ QUESTIONS at the end of the page

• 1.6C Energy transferred by device = appliance power x time

  • The total energy transferred by an electrical appliance depends on the power of the appliance (in J/S = W) and the time it is used for ... giving the simple proportionality formula ...

  • E = Pt (but focussing on its 'electrical' connection, not platinum!)

    • E energy in J, P power in W or J/s, t time in s

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

  • It is better to be able to rearrange a formula rather than using a triangle

  • Application: power of appliance = electrical energy transferred / time used

  • Formula connection: Since P = IV, substituting for P gives energy transferred E = IVt

    • When electrical charge moves through a potential difference energy is transferred as work done against the electrical resistance (p.d.).

    • The energy of the charge comes from the power source (dc battery, ac mains electricity) which raises the potential energy of the electrons.

    • The charge, (usually electrons), 'falls'  through the p.d. across the components of a circuit, giving up its electrical potential energy to another energy store e.g. thermal, or other form of energy e.g. sound or light.

    • The energy transferred in an electrical device can be calculated from the formula:

    • energy transferred in joules = current in amps x potential difference in volts x time in seconds

    • E (J) = I (A) x V (V) x t (s),   E = IVt

    • If you increase the p.d. or the current flowing through a circuit, the more energy you can transfer in a given time.

  • You can use two different sets of units

  • (1st) The usual and familiar J, W and s.

    • E is energy transferred in joules, J

    • P is power in watts, W = J/s

    • t is time in seconds, s

    • Examples of calculations

    • CQ1 An 800 watt oven is used for one and a half hours.

      • How much energy in MJ is transferred to the thermal energy store of the oven?

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    • CQ2 An electric heater transfers 1.5 MJ of energy every minute.

      • Calculate the power of the electric fire in kW.

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    • CQ3 A rechargeable battery can deliver a total of 8.0 MJ of energy to a device.

      • If the device delivers a power output of 25 W, to the nearest hour, how long can it be used for?

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    • CQ4 The p.d. across a resistor is 24.0 V. If a current of 3.0 A is flowing, how much energy is transferred in 5 minutes?

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    • CQ5 A 1200 W toaster is used for a total of 10 minutes.

      • How much energy is transferred in this time?

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    • CQ6 An appliance transfers 180 000 J of energy in two minutes.

      • Calculate the power of the appliance.

    • ANSWERS to CQ QUESTIONS at the end of the page

• 1.6D The kilowatt-hour and cost of electricity

  • The practical everyday units e.g. on an appliance or electricity bill.

  • 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

  • Power equation: P = E/t,  E = P x t,  t = E/P

• It is better to be able to rearrange a formula rather than using a triangle

• 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).

  • units of electricity are measured in kilowatt-hours e.g. for an appliance

  • kilowatt-hours = power in kW x time appliance used in hours

  • It is a measure of the energy transferred, and since 1 W = 1 J/s

  • 1 kWh = 1000 W x 3600 seconds = 3.6 X 10⁶ J = 3.6 MJ

• 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)

  • DQ1 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?

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    • (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?

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    • (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?

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

      • ANSWERS to DQ1 QUESTIONS at the end of the page

DQ2 More examples of cost calculations:

One unit of electricity is equal to using a 1000W (a power of 1kW) appliance for 1 hour.

The cost  of electricity (in 2022) has rocketed since I first designed these questions in 2002)

(a) What is the cost of using a 1.5kW heater for 2 hours if the cost of electricity is 7p/unit?

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(b) What is the cost of using a 3 kW heater for 6 hours if the cost of electricity is 6p/unit?

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(c) What is the cost of using a 60W light bulb for 20 hours if the cost of electricity is 5p/unit?

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(d) What is the cost of using a 700W iron for 2.5 hours if the cost of electricity is 8p/unit?

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(e) What is the cost of using a 200W hair dryer for 10 minutes if the cost of electricity is 6p/unit?

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(f) What is the cost of using a 4kW oven for 5 hours if the cost of electricity is 7p/unit?

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