Electrical power and energyIB MYP Physics: Revision notes
Section 1
Electrical power
Power is the rate at which energy is transferred. It is measured in watts (W): one watt is one joule per second.
P = I × V
Since V = I × R, we can also write P = I² × R.
- P is power in watts (W)
- I is current in amperes (A)
- V is potential difference in volts (V)
- R is resistance in ohms (Ω)
Worked example: a kettle carries 8.0 A at 230 V. P = 8.0 × 230 = 1840 W.
Worked example: a 5.0 Ω resistor carries 2.0 A. P = I²R = 2.0² × 5.0 = 20 W.
In P = I²R, only the current is squared. Square the current first, then multiply by R.
Section 2
Energy transferred
The energy transferred by an appliance depends on its power and how long it is on.
E = P × t, so E = I × V × t
- E is energy in joules (J)
- P is power in watts (W)
- t is time in seconds (s)
Worked example: a 1840 W kettle runs for 3.0 minutes. t = 3.0 × 60 = 180 s. E = 1840 × 180 = 331 200 J.
Always convert the time into seconds when the power is in watts and the energy is in joules.
Section 3
Kilowatt-hours and cost
Electricity bills use a bigger unit of energy, the kilowatt-hour (kWh). It is the energy transferred by a 1 kW appliance running for 1 hour.
Energy (kWh) = power (kW) × time (h)
Cost = energy (kWh) × price per kWh
Worked example: a 2.0 kW air conditioner runs for 6.0 h. Energy = 2.0 × 6.0 = 12 kWh. At 10 cents per kWh the cost is 12 × 10 = 120 cents.
For kWh, use the power in kilowatts (divide watts by 1000) and the time in hours.
Do not mix the units: joules go with watts and seconds, kWh goes with kilowatts and hours.
Section 4
Efficiency of appliances
No appliance transfers all the energy it receives into useful energy. Some is wasted, usually as thermal energy.
Efficiency = useful energy output ÷ total energy input (× 100% for a percentage)
Worked example: a heater receives 18 000 J of electrical energy and the water gains 13 500 J. Efficiency = 13 500 ÷ 18 000 = 0.75, or 75%.
Efficiency can never be more than 100%. A more efficient appliance wastes less energy and is cheaper to run.
Section 5
Electrical heating
When a current passes through a resistor, the electrons collide with the atoms of the wire. Energy is transferred as thermal energy, and the wire gets hot. This is the heating effect of a current.
The heating is useful in kettles, toasters and heaters. It is wasteful in connecting wires and in filament lamps, where most of the energy heats the air instead of giving light.
A larger current or a larger resistance gives a larger power, because P = I²R.
That's the notes covered.
Carry on to the next subtopic.
Exam questions on Electrical power and energy
- A café owner in Istanbul buys a new electric kettle. The label on the base states that it is designed for the 230 V mains supply. While testing it, she finds that the kettle draws a steady current of 8.0 A when switched on.The kettle has a power of 1840 W. Calculate the energy it transfers in 3.0 minutes.2 marks
- A family in Cairo has a 2.0 kW air conditioner. They run it for 6.0 hours every day. Their electricity supplier charges 10 cents for each kilowatt-hour (kWh) of energy.Calculate the cost of running the air conditioner for 30 days.2 marks
- A student investigates how efficiently an electric heater warms water. She connects a 12 V heater, which carries a current of 5.0 A, to a beaker of water and switches it on for 5.0 minutes. She then measures how much thermal energy the water has gained.Calculate the power of the heater and the electrical energy transferred to it in 5.0 minutes.3 marks
Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).