Power and Resistance

Section 1 of 7What electrical power means

Definition

• Definition Power is the rate at which energy is transferred, so a device with a higher power transfers more energy every second.
• It is measured in watts (W), where 1 W = 1 J/s.

Quantities involved

• Quantities involved P is power in watts (W), I is current in amperes (A), V is potential difference in volts (V) and R is resistance in ohms (Ω).
• Always list the known quantities with their symbols before choosing an equation.

Section 2 of 7Equations for power

Equation	Use it when you know	Tier
P = I × V	Current and potential difference	Foundation and Higher
P = V × I rearranged: I = P ÷ V	Power and potential difference, to find current	Foundation and Higher
P = I2 × R	Current and resistance	Higher only (HT only)
P = E ÷ t	Energy transferred and time taken	Foundation and Higher

Section 3 of 7Where P = I²R comes from (HT only)

1Start with P = IV

• Start with P = IV Power is current multiplied by potential difference.

2Replace V using Ohm's law

• Replace V using Ohm's law Since V = I × R, the potential difference can be written in terms of current and resistance.

3Substitute

• Substitute P = I × (I × R), which simplifies to P = I²R.

4Consequence

• Consequence For a fixed resistance, doubling the current makes the power four times as great, because the current is squared.

Section 4 of 7Worked example (HT only)

1

Question: a current of 6 A passes through a fixed 20 Ω resistor. Calculate its power.

2

List the knowns: I = 6 A and R = 20 Ω.

3

Choose the equation that uses I and R: P = I² × R.

4

Substitute: P = 6² × 20 = 36 × 20 = 720 W.

Section 5 of 7Choosing the right equation

Given R and I

• Given R and I Use P = I²R (HT only).

Given I and V

• Given I and V Use P = IV, which needs no resistance value.

Heating effect

• Heating effect A larger resistance or a larger current produces more energy transferred as heat each second,
  • which is why thin wires and heating elements get hot.

Section 6 of 7Key terms

Term	Meaning
Power	The rate of energy transfer, measured in watts (W).
Watt (W)	The unit of power; one joule transferred every second.
Current	The rate of flow of electric charge, measured in amperes (A).
Potential difference	The energy transferred per unit charge between two points, measured in volts (V).
Resistance	How strongly a component opposes current, measured in ohms (Ω).

Section 7 of 7Exam technique

1

Forgetting to square the current in P = I²R — squaring 6 A gives 36, not 12.

2

Squaring the whole product I × R instead of only the current.

3

Saying that doubling the current doubles the power; with a fixed resistance it quadruples it.

4

Skipping the list of known quantities, which makes it harder to pick the correct power equation.