GCSE Physics - How to Solve: Electrical Power, Energy Transfers, and Cost of Electricity

How to Solve: Electrical Power, Energy Transfers, and Cost of Electricity

Complete Guide (GCSE / A-Level Physics, Chemistry, Biology – Exam-Ready!)

Introduction

"Mastering electrical power and energy costs could save you 5–10 marks on your GCSE Physics paper—and help you calculate how much your gaming PC is really costing your parents!"

WHAT YOU NEED TO KNOW FIRST

Before starting, you must understand:
1. Current (I) – Flow of charge (Amps, A).
2. Potential Difference (V) – Energy per unit charge (Volts, V).
3. Resistance (R) – Opposition to current (Ohms, Ω).

(If you’re shaky on these, pause and review Ohm’s Law first!)

KEY TERMS & FORMULAS

Key Terms

Formulas

1. Power (P) = Current (I) × Potential Difference (V)
2. P = I × V (MEMORISE THIS!)

3. P (W), I (A), V (V)

4. Power (P) = Current² (I²) × Resistance (R)

5. P = I² × R (MEMORISE THIS!)

6. P (W), I (A), R (Ω)

7. Energy (E) = Power (P) × Time (t)

8. E = P × t (MEMORISE THIS!)

9. E (J), P (W), t (s)

10. Energy in kWh = Power (kW) × Time (h)

11. E (kWh) = P (kW) × t (h) (MEMORISE THIS!)

12. 1 kW = 1000 W

13. Cost = Energy (kWh) × Price per kWh

14. Cost = E × Price (MEMORISE THIS!)

(Note: P = V²/R is also useful but often given on exam sheets.)

STEP-BY-STEP METHOD

Follow these steps in order for every question:

1. Identify what’s given (e.g., current, voltage, time, cost per kWh).
2. Pick the right formula (check units—Watts or kW? Seconds or hours?).
3. Convert units if needed (e.g., W → kW, s → h).
4. Plug in numbers and calculate.
5. Check units in your answer (e.g., J, kWh, £).
6. Round to 2–3 significant figures (unless told otherwise).

WORKED EXAMPLES

Example 1 – Basic (Power Calculation)

A 12 V battery supplies 3 A to a motor. Calculate the power output.

Step 1: Given: V = 12 V, I = 3 A. Step 2: Use P = I × V. Step 3: No unit conversion needed. Step 4: P = 3 × 12 = 36 W. Step 5: Units = Watts (W). Step 6: Final answer: 36 W.

What we did and why: We used the simplest power formula because we had current and voltage.

Example 2 – Medium (Energy & Cost)

A 2 kW kettle boils water for 5 minutes. Electricity costs 15p per kWh. Calculate the cost.

Step 1: Given: P = 2 kW, t = 5 mins, cost = 15p/kWh. Step 2: Use E = P × t (but time must be in hours). Step 3: Convert 5 mins → 5/60 = 0.0833 h. Step 4: E = 2 × 0.0833 = 0.1666 kWh. Step 5: Cost = 0.1666 × 15 = 2.5 p. Step 6: Final answer: 2.5 pence.

What we did and why: We converted time to hours first because kWh requires hours. Then we multiplied energy by cost.

Example 3 – Exam-Style (Disguised Question)

A 6 Ω resistor has a current of 2 A for 300 seconds. Calculate the energy transferred in kJ.

Step 1: Given: R = 6 Ω, I = 2 A, t = 300 s. Step 2: First, find power using P = I² × R. Step 3: P = (2)² × 6 = 4 × 6 = 24 W. Step 4: Now, find energy using E = P × t. Step 5: E = 24 × 300 = 7200 J. Step 6: Convert J → kJ: 7200 ÷ 1000 = 7.2 kJ.

What we did and why: The question didn’t give power directly, so we had to calculate it first using resistance and current.

COMMON MISTAKES

1. MISTAKE: Using seconds instead of hours for kWh. WHY IT HAPPENS: Forgetting that kWh requires time in hours. CORRECT APPROACH: Always convert time to hours if using kWh.

2. MISTAKE: Confusing Watts (W) and kilowatts (kW). WHY IT HAPPENS: Not converting 2000 W → 2 kW. CORRECT APPROACH: Divide by 1000 if power is in Watts.

3. MISTAKE: Using P = I × V when resistance is given. WHY IT HAPPENS: Not checking which formula fits the given data. CORRECT APPROACH: If resistance is given, use P = I² × R or P = V²/R.

4. MISTAKE: Forgetting to convert pence to pounds (or vice versa). WHY IT HAPPENS: Not checking the required unit for cost. CORRECT APPROACH: If the answer needs £, divide pence by 100.

5. MISTAKE: Rounding too early. WHY IT HAPPENS: Rounding 0.0833 h → 0.1 h too soon. CORRECT APPROACH: Keep full decimals until the final step.

EXAM TRAPS

1. TRAP: Giving power in Watts but asking for energy in kWh. HOW TO SPOT IT: The question mentions "kWh" but gives power in W. HOW TO AVOID IT: Convert W → kW before calculating energy.

2. TRAP: Hiding resistance in a circuit diagram. HOW TO SPOT IT: The question shows a circuit with a resistor but doesn’t label R. HOW TO AVOID IT: Use V = I × R to find resistance first if needed.

3. TRAP: Asking for cost but giving time in minutes. HOW TO SPOT IT: The question says "5 minutes" but expects a cost in pence. HOW TO AVOID IT: Always convert time to hours for kWh.

1-MINUTE RECAP

"Right, listen up—this is your 60-second crash course for electrical power and energy costs. First, memorise these three formulas: P = I × V, E = P × t, and Cost = Energy × Price per kWh. If you see resistance, use P = I² × R. Always check units—Watts or kilowatts? Seconds or hours? Convert before you calculate. For cost questions, time must be in hours, and energy in kWh. Watch out for examiners hiding resistance or giving time in minutes. Round at the end, not before. And if you’re stuck, write down what you know and pick the formula that fits. You’ve got this—go smash that exam!"