E5: Power & Energy in Circuits
P=VI, P=I²R, energy dissipation, battery capacity and efficiency
Power & Energy in Circuits
P=VI, P=I²R, energy dissipation, battery capacity and efficiency
Key Fact: Electrical power P = VI, measured in watts (W); 1 W = 1 J/s.
Key Fact: Using Ohm's Law, power can also be expressed as P = I²R or P = V²/R.
Key Fact: Electrical energy E = Pt, measured in joules (J); domestic energy is billed in kWh.
Key Fact: Resistors dissipate power as heat; this must be within the resistor's power rating to avoid damage.
Key Fact: Battery capacity is measured in amp-hours (Ah); a 2000 mAh battery can deliver 2 A for 1 hour.
Key Fact: Efficiency = useful power output / total power input, expressed as a percentage.
Key Fact: Energy lost as heat reduces efficiency; minimizing resistance in conductors reduces waste.
Key Fact: The total power supplied by a source equals the sum of power dissipated in all components.
Key Fact: Fuses are rated by current; they melt when power dissipation causes excessive temperature.
Key Fact: In AC circuits, power factor affects the real power delivered: P_real = VI cos φ.
Key Fact: A battery's internal resistance causes a voltage drop under load, reducing useful power output.
Key Fact: Energy conservation: energy supplied = energy stored + energy dissipated as heat.
📋 Key Vocabulary and Concepts
For Power & Energy in Circuits, you must know:
- Power: The rate at which energy is transferred or dissipated, measured in watts.
- Energy: The capacity to do work, measured in joules; E = Pt.
- Amp-hour (Ah): A unit of battery capacity; 1 Ah = 3600 C of charge.
- Efficiency: The ratio of useful output power to total input power, expressed as a percentage.
- Internal resistance: The resistance within a battery that causes voltage drop under load.
- Power rating: The maximum power a component can safely dissipate without damage.
❓ Practice Questions
Q: A 12 V supply delivers 5 A. What is the power?
Q: A 10 Ω resistor carries 2 A. What power does it dissipate?
Q: A 60 W lamp runs for 3 hours. How much energy does it consume?
Q: A 3000 mAh battery powers a device drawing 150 mA. How long will it last?
Q: A circuit has 100 W input power and 75 W useful output. What is the efficiency?
✅ Answers
- P = VI = 12 × 5 = 60 W.
- P = I²R = 2² × 10 = 40 W.
- E = Pt = 60 × 3 = 180 Wh = 0.18 kWh.
- Time = capacity/current = 3000/150 = 20 hours.
- Efficiency = 75/100 × 100% = 75%.
🎯 Exam Tips
- Choose the correct power formula: use P = VI if V and I are known, P = I²R if I and R are known, P = V²/R if V and R are known.
- Convert mAh to Ah (divide by 1000) before calculating battery life.
- Always check power ratings of resistors; a ¼ W resistor cannot safely dissipate 2 W.
- For efficiency, state the formula first: η = P_out/P_in × 100%.
- When a battery has internal resistance, use V_terminal = EMF − I × r_internal.
📝 Exam Technique
GCSE Electronics Exam Tips — Power & Energy in Circuits:
1. For Power & Energy in Circuits questions, use correct electronic symbols and terminology
2. Always show your working in calculations, including units at each step
3. When analysing circuits, state which law or rule you are applying first
4. For evaluation questions on Power & Energy in Circuits, compare component choices and consider cost, reliability and tolerance
5. Draw circuit diagrams neatly with conventional symbols
1. For Power & Energy in Circuits questions, use correct electronic symbols and terminology
2. Always show your working in calculations, including units at each step
3. When analysing circuits, state which law or rule you are applying first
4. For evaluation questions on Power & Energy in Circuits, compare component choices and consider cost, reliability and tolerance
5. Draw circuit diagrams neatly with conventional symbols
⚠️ Common Errors
✗ Using P = IR instead of P = I²R. ✓ The correct formulae are P = VI, P = I²R, and P = V²/R.
✗ Confusing energy (joules or kWh) with power (watts). ✓ Power is the rate of energy transfer (W = J/s); energy is power × time.
✗ Forgetting to convert mAh to Ah when calculating battery life. ✓ Divide mAh by 1000 to get Ah before using time = capacity/current.
✗ Assuming all input power is useful output power. ✓ Some power is always lost as heat; efficiency = useful output / total input.
✍️ Model Answer
Full-Mark Response
Explain the relationship between power, voltage, current and resistance in a circuit, and discuss how energy efficiency is affected by internal resistance.
Power in an electrical circuit is the rate of energy transfer, calculated as P = VI. By substituting Ohm's Law (V = IR), two alternative forms are derived: P = I²R and P = V²/R. The choice of formula depends on which quantities are known. Energy consumed is E = Pt, measured in joules or kilowatt-hours for domestic billing. Internal resistance in a battery causes a voltage drop V_lost = I × r_internal when current is drawn, reducing the terminal voltage available to the load. This means some power (I² × r_internal) is dissipated inside the battery as heat rather than being delivered to the circuit. The useful output power is therefore less than the total power from the EMF, reducing efficiency. High-current applications are most affected because internal resistance losses increase with the square of current (P = I²R). To maximise efficiency, batteries with low internal resistance should be used, and load resistance should be significantly greater than the internal resistance.
📊 AO Deep Dive
Assessment Objective Analysis
AO1 (Knowledge & Understanding): Demonstrate knowledge and understanding of power & energy in circuits, including electronic components, circuit theory and systems concepts relevant to WJEC Eduqas C690QS.
AO2 (Application): Apply knowledge and understanding of power & energy in circuits to analyse, design and construct electronic circuits and systems.
AO3 (Evaluation): Evaluate electronic circuits and systems, making reasoned judgements about design choices, performance and practical considerations, constructing supported arguments.
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