Electricity and Power

Section 1 of 9Electrical power

Definition

• Definition Power is the rate of energy transfer: the energy transferred each second.

What decides it

• What decides it For an electrical device, the power depends on the potential difference across it and the current through it.

Unit

• Unit The watt, W, which equals one joule per second.

Section 2 of 9Power equations

Equation	Use when you know	Symbols
P = I × V	current and potential difference	P in W, I in A, V in V
P = I2 × R	current and resistance	R in ohms (Ω)
P = V2 ÷ R	potential difference and resistance	Derived from the other two

Section 3 of 9Where P = I2R comes from

1Start

• Start P = I × V.

2Use Ohm's law

• Use Ohm's law V = I × R.

3Substitute

• Substitute P = I × (I × R).

4Result

• Result P = I² × R. Doubling the current quadruples the power for the same resistance.

Section 4 of 9Worked examples

1

Find V for a 48 W motor carrying 4 A: rearrange P = I × V to V = P ÷ I = 48 ÷ 4 = 12 V.

2

Find P for a 20 Ω resistor with 6 A through it: P = I² × R = 6² × 20 = 36 × 20 = 720 W.

3

Choose the equation that matches the two quantities you are given.

4

Square the current first, and only then multiply by the resistance.

Section 5 of 9Selecting the correct equation

Which power equation?

I and V given

• I and V given Use P = I × V.

I and R given

• I and R given Use P = I² × R.

Units check

• Units check Watts from amps and volts: A × V = W.

Section 6 of 9Worked example: a heating coil

Stage	Working	Result
Given	A coil of resistance 15 Ω carries 3 A	I = 3 A, R = 15 Ω
Equation	P = I2 × R	P = 32 × 15
Square	32 = 9	P = 9 × 15
Answer	Multiply and add the unit	P = 135 W

Section 7 of 9Why the current is squared

Effect of doubling the current

• Effect of doubling the current Because power depends on I², doubling the current multiplies the power by four,
  • and trebling it multiplies the power by nine.

Link to power cables

• Link to power cables This is why a large current in a thin cable produces so much heating,
  • and why cables carrying large currents have a low resistance.

Rearranging

• Rearranging To find the current: I = √(P ÷ R).
  • To find the resistance: R = P ÷ I².
  • Take the square root only at the very end.

Section 8 of 9Key terms

Term	Meaning
Power	Energy transferred per second; measured in watts.
Potential difference	Energy transferred per unit charge, measured in volts.
Current	Rate of flow of charge, measured in amperes.
Resistance	Opposition to current, measured in ohms; V = I × R.
Ohm's law	For an ohmic conductor at constant temperature, V = I × R.

Section 9 of 9Exam technique

1

Multiplying the current by the resistance instead of squaring the current first.

2

Writing P = I × R, missing the square.

3

Using the wrong rearrangement, e.g. V = P × I rather than V = P ÷ I.

4

Quoting the answer in joules rather than watts.