A 5 A Circuit, a Heater and a Missing Earth Wire
A household is supplied at 230 V through two circuits: a 5 A lighting circuit and a 15 A power circuit. On the lighting circuit are a 100 W bulb, a 60 W bulb and a 40 W tube light. A visitor plugs a 1,500 W room heater into a multiplug on the same lighting circuit. The fuse in that circuit is a 5 A fuse. In the kitchen, a washing machine on the 15 A circuit has a worn live wire touching its metal body; the earth wire in its plug has been cut off 'because it kept tripping'. A person touches the machine while standing on a wet floor and receives a severe shock. The main fuse does not blow. The owner says the 5 A fuse will protect the heater and the 15 A fuse will protect the person.
1. Calculate the current drawn by the heater alone and by the whole lighting circuit with the heater, and predict what the 5 A fuse does. Show your reasoning.
Read the worked answer
Heater alone: I = P/V = 1500/230 ≈ 6.5 A.
Lighting load: 100 + 60 + 40 = 200 W, so I = 200/230 ≈ 0.87 A.
Total with heater: 0.87 + 6.5 ≈ 7.4 A, which exceeds the 5 A fuse rating. Even the heater alone exceeds 5 A, so the circuit is overloaded before the lights are counted.
Prediction: the 5 A fuse should melt and break the circuit. A fuse does not act instantly at a small overload; it has an inverse-time characteristic, so a 7.4 A current may take some time to melt a 5 A fuse, during which the wiring and multiplug heat up. If the fuse does not blow, the fault is not that the load is safe - it is that the fuse or the wiring is defective. The owner's first statement is therefore only partly right: the fuse is intended to protect the cable, and it is being asked to carry a load beyond its rating.
2. Explain why the 15 A fuse did not blow when the person touched the washing machine, and why the earth wire would have changed the outcome.
Read the worked answer
When the live wire touches the metal body and the earth wire is cut, the body becomes live. The person touching it and standing on a wet floor completes a path to earth through their body. Body resistance under wet conditions may be only about 1–5 kΩ, so the current through the person is roughly 230/1000 to 230/5000, i.e. about 46–230 mA - dangerous to life but far below 15 A. A 15 A fuse responds to a large overcurrent, not to a small leakage through a person, so it does not blow.
An intact earth wire would have provided a low-resistance metal path from the body to earth. The fault current would then be large, because the supply is effectively shorted to earth through a low-resistance conductor, and the 15 A fuse or the circuit breaker would operate quickly. The person would be bypassed because the earth path has far lower resistance than the body. Earthing is therefore a protective measure, not an optional extra.
3. The owner wants to replace the 5 A fuse with a 10 A fuse and reconnect the earth wire to a water pipe. Assess both actions.
Read the worked answer
10 A fuse on the lighting circuit: unsafe. The fuse is chosen to protect the cable, not the appliance. A 10 A fuse allows a current that the lighting cable may not be able to carry without overheating, so the risk shifts from a blown fuse to overheated insulation and fire. The correct response is to move the heater to the 15 A power circuit, not to enlarge the fuse.
Earthing to a water pipe: unreliable and potentially dangerous. Metal water pipes are not a guaranteed earth electrode; sections may be plastic, joints may be sealed with tape or compound, and the pipe may be disconnected during repairs. A fault current could then energise the plumbing, and anyone touching a tap could receive a shock. The earth wire must run to a proper earth electrode or the installation's earth terminal.
Neither action addresses the real hazard. A residual-current device of about 30 mA sensitivity would protect people against earth leakage, whereas fuses and overload breakers primarily protect wiring.