1. Overview
This topic explores how electrical circuits serve as a system for transferring energy from a power source (like a battery or the mains) to various components where it is converted into useful forms, such as light or heat. Understanding these calculations allows us to determine the efficiency of appliances and calculate the financial cost of the electricity we consume at home.
Key Definitions
- Electrical Power ($P$): The rate at which electrical energy is transferred by a circuit or a component.
- Electrical Energy ($E$): The total amount of work done by an electric current over a period of time.
- Watt (W): The SI unit of power, equivalent to one Joule per second ($1\text{ J/s}$).
- Kilowatt-hour (kWh): A unit of energy representing the energy used by a $1\text{ kW}$ appliance running for $1\text{ hour}$.
- Mains Supply: The general-purpose alternating current (AC) electric power supply provided to homes and businesses.
Core Content
Energy Transfer in Circuits
Electric circuits are energy transfer systems.
- The Source: An electrical cell, battery, or the mains supply provides the energy.
- The Transfer: Electrons flow through the circuit, carrying this energy.
- The Components: Components like lamps (light), heaters (thermal), or motors (kinetic) convert the electrical energy into other forms.
- The Surroundings: Eventually, most of this energy is dissipated into the surroundings, usually as heat.
Electrical Power
Power is calculated using the current and potential difference (voltage) across a component.
- Formula: $P = I \times V$
- A simple circuit containing a battery, an ammeter in series, and a voltmeter in parallel across a bulb to show how $I$ and $V$ are measured.
Worked Example: A toaster is connected to a $230\text{V}$ mains supply. If the current flowing through it is $4\text{A}$, what is the power?
- $P = I \times V$
- $P = 4\text{A} \times 230\text{V} = 920\text{W}$
Electrical Energy
Energy is power multiplied by time. In standard SI units, time must be in seconds.
- Formula: $E = P \times t$ (or $E = I \times V \times t$)
Worked Example: How much energy is transferred by a $60\text{W}$ bulb left on for $5$ minutes?
- Convert time to seconds: $5 \times 60 = 300\text{s}$
- $E = P \times t = 60\text{W} \times 300\text{s} = 18,000\text{J}$ (or $18\text{kJ}$)
The Kilowatt-hour (kWh) and Cost
Electricity companies measure energy in kilowatt-hours because Joules are too small for household bills.
- $1\text{ kWh} = \text{Power (in kW)} \times \text{Time (in hours)}$
- $\text{Total Cost} = \text{Energy used (in kWh)} \times \text{Price per unit}$
Worked Example: An air conditioner rated at $2\text{kW}$ is used for $10$ hours. If $1\text{kWh}$ costs $$0.15$, what is the total cost?
- $\text{Energy} = 2\text{kW} \times 10\text{h} = 20\text{kWh}$
- $\text{Cost} = 20\text{kWh} \times $0.15 = $3.00$
Extended Content (Extended Only)
There are no specific supplemental requirements for section 4.2.5; all students should focus on the core objectives listed above.
Key Equations
| Word Equation | Symbol Equation | Units |
|---|---|---|
| $\text{Power} = \text{Current} \times \text{Voltage}$ | $P = I \times V$ | Watts (W), Amps (A), Volts (V) |
| $\text{Energy} = \text{Power} \times \text{Time}$ | $E = P \times t$ | Joules (J), Watts (W), Seconds (s) |
| $\text{Energy (kWh)} = \text{Power (kW)} \times \text{Time (h)}$ | $E = P \times t$ | kWh, Kilowatts (kW), Hours (h) |
Common Mistakes to Avoid
- ❌ Wrong: Using minutes or hours when calculating energy in Joules. ✓ Right: Always convert time to seconds ($1\text{ minute} = 60\text{s}$) unless calculating kWh.
- ❌ Wrong: Calculating cost using Power in Watts. ✓ Right: Divide Watts by $1000$ to get Kilowatts (kW) before calculating kWh (e.g., $500\text{W} = 0.5\text{kW}$).
- ❌ Wrong: Stating that a fuse provides a path to earth. ✓ Right: The Earth wire provides a path to earth; the fuse is a safety device that melts and breaks the circuit if current is too high.
- ❌ Wrong: Confusing logic gate symbols in electricity diagrams. ✓ Right: Remember that an AND gate has a flat input side and a D-shaped output; do not confuse it with OR gates.
- ❌ Wrong: Forgetting that standard mains voltage is $230\text{V}$ (in many exam contexts) and using incorrect values.
Exam Tips
- Check your units first: Before starting a calculation, look at the units provided. If the question asks for Energy in Joules but gives time in minutes, convert to seconds immediately.
- Show your working: In kWh cost questions, examiners often give marks for the intermediate step of converting Power from Watts to Kilowatts.
- Identify the relationship: If a question gives you Current and Voltage but asks for Energy, remember you must first find Power ($P=IV$) and then multiply by time ($E=Pt$).