Electrical Power and Energy

This lesson covers electrical power and energy transfer calculations — as required by the Edexcel GCSE Physics specification (1PH0). You need to be confident using several key equations, converting between units, and calculating electricity costs. These topics appear frequently in exam calculations.

Electrical Power

Power is the rate of energy transfer — it tells you how much energy a device transfers per second.

Key Equations for Power

There are three equations you need to know:

Equation 1:

$P = IV$

Where:

P = power (watts, W)
I = current (amperes, A)
V = potential difference (volts, V)

Equation 2:

$P = I^2 R$

Where:

P = power (watts, W)
I = current (amperes, A)
R = resistance (ohms, Ω)

Equation 3:

$P = \frac{V^2}{R}$

Where:

P = power (watts, W)
V = potential difference (volts, V)
R = resistance (ohms, Ω)

How the Equations Are Related

All three can be derived from P = IV and V = IR:

graph TD
    A["P = IV"] --> B["Substitute V = IR"]
    B --> C["P = I × IR = I²R"]
    A --> D["Substitute I = V/R"]
    D --> E["P = V/R × V = V²/R"]

    style A fill:#2c3e50,color:#fff
    style B fill:#2980b9,color:#fff
    style C fill:#27ae60,color:#fff
    style D fill:#2980b9,color:#fff
    style E fill:#27ae60,color:#fff

Units

Quantity	Symbol	Unit	Unit Symbol
Power	P	watt	W
Current	I	ampere	A
Voltage	V	volt	V
Resistance	R	ohm	Ω

1 watt = 1 joule per second (1 W = 1 J/s)

Larger units: 1 kilowatt (kW) = 1000 W

Exam Tip: Choose the power equation that matches the quantities you are given. If you know I and V, use P = IV. If you know I and R, use P = I²R. If you know V and R, use P = V²/R. Selecting the right equation avoids unnecessary steps.

Energy Transferred

Key Equations for Energy

Equation 1:

$E = Pt$

Where:

E = energy transferred (joules, J)
P = power (watts, W)
t = time (seconds, s)

Equation 2:

$E = QV$

Where:

E = energy transferred (joules, J)
Q = charge (coulombs, C)
V = potential difference (volts, V)

How They Relate

Since Q = It, we can write: E = QV = (It)V = IVt = Pt

Both equations give the same result — use whichever matches the information given.

Unit Conversions

Time Conversions

From	To	Multiply By
Minutes	Seconds	× 60
Hours	Seconds	× 3600
Hours	Minutes	× 60

Power Conversions

From	To	Multiply By
kW	W	× 1000
W	kW	÷ 1000

Exam Tip: A very common mistake is forgetting to convert units. If the question gives power in kW, you may need to convert to W before using E = Pt (if the answer is required in joules). If the question asks for energy in kWh, keep power in kW and time in hours.

The Kilowatt-Hour (kWh)

The kilowatt-hour (kWh) is the unit of energy used by electricity companies on your bill. It is not a unit of power.

1 kWh = the energy transferred by a 1 kW device in 1 hour.

Calculating Energy in kWh

$E \text{ (kWh)} = P \text{ (kW)} \times t \text{ (hours)}$

Converting Between kWh and Joules

$1 \text{ kWh} = 1000 \text{ W} \times 3600 \text{ s} = 3{,}600{,}000 \text{ J} = 3.6 \times 10^6 \text{ J} = 3.6 \text{ MJ}$

Calculating Electricity Costs

$\text{Cost} = \text{Energy (kWh)} \times \text{Price per kWh (p)}$

Or equivalently:

$\text{Cost} = P \text{ (kW)} \times t \text{ (hours)} \times \text{Price per kWh}$

Worked Examples

Example 1: Calculate Power

A 230 V kettle draws a current of 10 A. What is its power?

P = IV = 10 × 230 = 2300 W (or 2.3 kW)

Example 2: Calculate Power Using P = I²R

A current of 4 A flows through a 10 Ω heating element. What is the power?

P = I²R = 4² × 10 = 16 × 10 = 160 W

Example 3: Calculate Energy Transferred

A 2 kW heater is used for 3 hours. How much energy does it transfer?

In kWh: E = P × t = 2 × 3 = 6 kWh

In joules: E = 6 × 3.6 × 10⁶ = 2.16 × 10⁷ J

Example 4: Calculate the Cost

A 3 kW oven is used for 2.5 hours. Electricity costs 30p per kWh. What is the cost?

E = 3 × 2.5 = 7.5 kWh Cost = 7.5 × 30 = 225p (or £2.25)

Example 5: Energy Using E = QV

A charge of 500 C passes through a 12 V power supply. How much energy is transferred?

E = QV = 500 × 12 = 6000 J

Example 6: Multi-Step Problem

A 60 W lamp is connected to a 230 V supply. Calculate the current and the energy transferred in 10 minutes.

Current: I = P / V = 60 / 230 = 0.26 A (2 s.f.)

Energy: First convert time: 10 min = 600 s E = Pt = 60 × 600 = 36,000 J (or 36 kJ)

Exam Tip: When a question involves multiple steps, write down each step clearly and show your working. State the equation you are using, substitute the values, and give the answer with correct units. This is how you earn method marks even if the final answer is incorrect.

Electrical Power and Energy

Electrical Power and Energy