Electrical Power & Energy

P = VI, P = I²R | E = Pt | Kilowatt-hours & Cost of Electricity

AQA GCSE Physics 4.2 | Year 10 | Foundation & Higher

⚡ State what electrical power means and give its unit (watt, W)

🔢 Use P = VI and P = I²R to calculate electrical power

⏱️ Use E = Pt to calculate electrical energy transferred

🔌 Understand appliance power ratings and what they tell us

💡 Convert between joules and kilowatt-hours (kWh)

💰 Calculate the cost of electricity using energy and unit price

⚡ What is Electrical Power?

Power is the rate at which energy is transferred (or work is done). In electrical circuits, power tells us how quickly a device converts electrical energy into other forms — such as heat, light, sound or kinetic energy.

Electrical Power (P): The rate of energy transfer in an electrical component or circuit. Measured in watts (W), where 1 W = 1 J/s.

A higher-powered appliance transfers more energy every second. For example, a 2000 W kettle transfers 2000 joules of electrical energy into heat every second — much faster than a 60 W light bulb.

P = E ÷ t
Power (W) = Energy transferred (J) ÷ Time (s)

Symbol	Quantity	Unit
P	Power	Watt (W)
E	Energy transferred	Joule (J)
t	Time	Second (s)

1 kilowatt (kW) = 1000 W | 1 megawatt (MW) = 1 000 000 W

🔢 Power Equations: P = VI and P = I²R

We can also express power in terms of the current and voltage in a circuit. Using Ohm's Law (V = IR), we can derive two very useful power equations:

P = V × I
Power (W) = Voltage (V) × Current (A)

This equation says that power depends on both how large the voltage is and how much current flows. Doubling the voltage while keeping current constant doubles the power.

P = I² × R
Power (W) = Current² (A²) × Resistance (Ω)

This form is especially useful when we know the current and resistance but not the voltage directly. Notice that power increases with the square of the current — doubling the current quadruples the power dissipated in a resistor. This is why large currents are so dangerous and why fuses protect circuits.

Symbol	Quantity	Unit
P	Power	Watt (W)
V	Voltage (potential difference)	Volt (V)
I	Current	Ampere (A)
R	Resistance	Ohm (Ω)

Higher Tier: You may be asked to derive P = I²R from P = VI and V = IR. Substitute V = IR into P = VI to get P = (IR) × I = I²R.

⏱️ Energy Transferred: E = Pt

Rearranging P = E ÷ t gives us a formula to calculate the total energy transferred by an electrical appliance over a given time:

E = P × t
Energy (J) = Power (W) × Time (s)

This is crucial for understanding electricity bills, comparing appliances and calculating running costs. Note that time must be in seconds when using joules as the energy unit.

We can also combine this with P = VI to get:

E = V × I × t
Energy (J) = Voltage (V) × Current (A) × Time (s)

Energy transferred is the total electrical energy converted into other forms (heat, light, sound, etc.) by a device over a period of time.

Always check your units! If time is given in minutes, multiply by 60 to convert to seconds before using E = Pt with joules.

💡 Kilowatt-Hours and Appliance Ratings

For everyday electricity use, the joule is a tiny unit — a kettle boiling for 3 minutes transfers roughly 360 000 J. Instead, electricity suppliers use the kilowatt-hour (kWh).

1 kilowatt-hour (kWh) is the energy transferred by a 1 kW appliance running for 1 hour.
1 kWh = 1000 W × 3600 s = 3 600 000 J = 3.6 × 10⁶ J

E (kWh) = P (kW) × t (hours)
Energy in kilowatt-hours = Power in kilowatts × Time in hours

Appliance power ratings tell us the rate at which a device transfers energy under normal operating conditions. Examples:

Appliance	Typical Power Rating
LED bulb	8 W
Phone charger	5–20 W
Laptop	45–65 W
Television	100–200 W
Microwave	800–1200 W
Electric kettle	2000–3000 W
Electric oven	2000–2500 W
Electric shower	7000–10 500 W

💰 Cost of Electricity

Electricity companies charge per kilowatt-hour (kWh) — often called a "unit" of electricity. To find the cost of running an appliance:

Cost = E (kWh) × price per kWh (p or £)
Cost (p) = Energy used (kWh) × Price per unit (p/kWh)

As of recent UK energy prices, a typical unit cost is around 28–30 p per kWh (this changes with tariffs, so exam questions will give you a price).

Step-by-step approach to cost questions:
1. Convert power to kW (divide W by 1000)
2. Calculate energy: E = P (kW) × t (hours)
3. Calculate cost: Cost = E (kWh) × price per kWh

Understanding electricity costs helps us make informed choices — for instance, switching from a 60 W incandescent bulb to an 8 W LED bulb uses about 87% less energy, saving money and reducing carbon emissions.

Kilowatt-hour (kWh): The commercial unit of electrical energy. Used on electricity bills. 1 kWh = 3.6 × 10⁶ J.

Example 1: A hairdryer operates at a voltage of 230 V and draws a current of 4.5 A. Calculate its power rating.

1 Identify the equation needed: P = V × I

2 Write down known values: V = 230 V, I = 4.5 A

3 Substitute: P = 230 × 4.5

4 Calculate: P = 1035 W

Power = 1035 W (approximately 1.0 kW)

Example 2: A resistor has a resistance of 25 Ω and a current of 3.0 A flows through it. Calculate the power dissipated in the resistor.

1 Identify the equation: P = I² × R

2 Known values: I = 3.0 A, R = 25 Ω

3 Calculate I² first: 3.0² = 9.0 A²

4 Substitute: P = 9.0 × 25 = 225 W

Power dissipated = 225 W

Example 3: A 2.0 kW electric kettle is used for 6 minutes. Calculate (a) the energy transferred in joules, and (b) the energy transferred in kWh.

1 Convert time to seconds: 6 min × 60 = 360 s

2 Convert power to watts: 2.0 kW = 2000 W

3 Use E = P × t: E = 2000 × 360 = 720 000 J

4 For kWh: convert time to hours: 6 ÷ 60 = 0.1 hours

5 E (kWh) = P (kW) × t (h) = 2.0 × 0.1 = 0.2 kWh

(a) Energy = 720 000 J | (b) Energy = 0.2 kWh

Example 4: A household uses a 3.0 kW electric oven for 2.5 hours. Electricity costs 28 p per kWh. Calculate the cost of using the oven.

1 Calculate energy used: E = P × t = 3.0 kW × 2.5 h = 7.5 kWh

2 Calculate cost: Cost = E × price per kWh = 7.5 × 28 p

3 Cost = 210 p = £2.10

Cost = 210 p (£2.10)

Question 1: Which equation correctly gives electrical power in terms of current and resistance?

Question 2: A lamp has a power rating of 60 W and runs for 5 hours. How many kWh of energy does it use?

Question 3: A toaster operates at 230 V with a current of 3.5 A. Calculate its power in watts. Enter your answer below.

Question 4: How many joules are in 1 kWh?

Question 5: A 1500 W heater runs for 3 hours. Electricity costs 30 p per kWh. Calculate the cost in pence.

Challenge 1 (Higher): A resistor dissipates 180 W of power when a current of 6.0 A flows through it. Calculate the resistance of the resistor. Show your working.

Challenge 2: A household has two televisions: TV A is rated at 180 W and TV B is rated at 85 W. Both are left on for 6 hours per day for 30 days. Electricity costs 29 p per kWh. Calculate the difference in electricity cost between the two TVs over the 30-day period.

Challenge 3 (Higher): An electric shower is rated at 9.5 kW and operates from the mains at 230 V. (a) Calculate the current drawn by the shower. (b) A fuse must be chosen that is just above the calculated current. Choose from: 5 A, 13 A, 30 A, 45 A.

Challenge 4 (Extended Answer): A student claims that replacing all the incandescent bulbs (60 W each) in a house with LED bulbs (8 W each) will save a large amount of money. There are 12 bulbs in total, used for an average of 5 hours per day. Electricity costs 28 p per kWh. Calculate the annual saving (365 days) and evaluate the student's claim.