Electricity in the
home: 1.6
Power, energy
transfer and electricity cost calculation
practice exam questions
with worked out answers
Doc Brown's Physics exam study revision notes
Exam practice questions on calculating power, energy transfer,
calculations, problem solving the costing of using
electrical power, calculating current flowing through an electrical
appliance, How to calculate the energy
transfers in an electrical appliance? What do
we mean by a unit of electricity used? How do we calculate the
cost of running an electrical device?
INDEX for physics notes on
electricity in the home
This page contains online questions only. Jot down
your answers and check them against the worked out answers at the end of
the page
ANSWERS to ALL the QUESTIONS at the end of the page
1.6a Power, energy
transfer and electricity cost calculation
QUESTIONS

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 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 = 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
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.

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.

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

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?

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

1.6B power = current^{2} x
resistance

P = IV and since V = IR,
substituting for V gives P = I^{2}R

P = I^{2}R

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 = I^{2}R
 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.

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

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

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!)

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.

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

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

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?

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

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

ANSWERS to CQ QUESTIONS at the end of the page

1.6D The
kilowatthour and cost of electricity

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

E is
energy transferred in kilowatthours, 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 kilowatthours (kWh) and units of time
in hours (h).

units of electricity are measured in
kilowatthours e.g. for an appliance

kilowatthours = 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 10^{6}
J = 3.6 MJ
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?

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

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

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

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

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

ANSWERS to DQ2 QUESTIONS at the end of the page
INDEX of ELECTRICITY Notes 1. Electricity in the home
Keywords, phrases and learning objectives for selected electricity calculations
Be able to do questions on calculating power, energy
transfer, unit costs of electricity.
Know how to solve problems on
costing of electrical power e.g. the cost of using an appliance for
a given time.
Know how to calculate the current flowing through an
appliance.
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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