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Question
An iron draws 5.0 A from a 230 V mains supply. Calculate its power.
Solution
Apply P = VI.
Answer
1150 W (1.15 kW).
Question
A wire of resistance 0.5 Ω carries 12 A. Calculate the power dissipated as heat.
Solution
Apply P = I²R.
Answer
72 W.
Question
A transmission cable has total resistance 5 Ω. Compare the power lost when transmitting 200 MW at 10 kV vs at 400 kV.
Solution
Current at 10 kV.
Loss at 10 kV.
Current at 400 kV.
Loss at 400 kV.
Answer
At 10 kV the loss exceeds the supplied power (impossible). At 400 kV the loss is just 1.25 MW (~0.6 %). High-voltage transmission is essential.
Examiner note
Use the I² term — it makes the case dramatic.
Question
A 900 W toaster operates for 90 s. Calculate the energy it transfers.
Solution
Apply E = Pt.
Answer
81,000 J (81 kJ).
Question
5.0 C of charge passes through a 12 V battery-powered drill. How much energy does the drill receive?
Solution
Apply E = QV.
Answer
60 J.
Question
Describe the energy transfers in an electric kettle, naming the relevant stores.
Solution
Input.
Useful.
Wasted.
Answer
Electrical → useful thermal store of water; wasted thermal stores of kettle, air; small sound radiation.
Question
100 MW must be transmitted along a 4 Ω cable. Calculate the power lost at (a) 10 kV, (b) 400 kV.
Solution
Current at 10 kV.
Loss at 10 kV.
Current at 400 kV.
Loss at 400 kV.
Answer
10 kV: 400 MW lost (more than transmitted). 400 kV: 0.25 MW (~0.25 %). High voltage transmission is essential.
Examiner note
Emphasise I² in the explanation.
Power (V and I)
When to use
Whenever V and I are given. Recall — not on equation sheet.
Power (I and R)
When to use
Use when I and R are known (e.g. power dissipated in a wire or resistor).
Energy (power and time)
When to use
When P and t are given.
Energy (charge and p.d.)
When to use
When Q and V are given. Derived from 1 V = 1 J/C.
The rate at which electrical energy is transferred in a circuit (W).
Energy transferred to the intended store (the appliance's purpose).
Energy dissipated to unintended stores, usually thermal store of the surroundings.
A transformer that increases the AC voltage (and decreases the current). Has more turns on its secondary coil than primary.
A transformer that decreases voltage (and increases current). Has fewer turns on secondary than primary.
The UK-wide network of cables, pylons and substations that distributes electricity from power stations to consumers.
Mistake
Forgetting to square I in P = I²R.
Why it happens
Quick substitution.
How to avoid it
Write P = I × I × R explicitly.
Mistake
Using P = VI when V is unknown but I and R are given.
Why it happens
Defaulting to the first formula.
How to avoid it
Choose the formula whose variables match what you have.
Mistake
Writing 'electrical energy store'.
Why it happens
Electrical is treated as a thing.
How to avoid it
Electrical is a transfer pathway, NOT a store. The relevant store is chemical (battery) or thermal/kinetic (in the appliance).
Mistake
Plugging time in minutes into E = Pt.
Why it happens
Forgetting to convert.
How to avoid it
Always convert to seconds first.
Mistake
Saying transformer increases the power.
Why it happens
Confusing V with P.
How to avoid it
Transformers conserve power (V_p I_p = V_s I_s). They TRADE voltage for current.
Mistake
Saying the National Grid is DC.
Why it happens
Confusion with HVDC links.
How to avoid it
GCSE answer is AC. Transformers need AC.