The Blown Fuse on a Cold Evening
A house is connected to a 220 V mains supply through a 20 A fuse. The appliances and their marked power ratings are: geyser 2000 W, room heater 1500 W, electric iron 750 W, refrigerator 200 W, four bulbs of 40 W each, one fan of 80 W, and a television of 100 W. On a cold evening the geyser, heater, iron, lights, fan, television and refrigerator are all switched on together. After about ten minutes the lights go out and the fuse has blown. The owner's neighbour says the simplest solution is to wind a few turns of thick copper wire round the fuse terminals, or to fit a 30 A fuse, because 'the fuse was too weak anyway'. The owner also wants to know why the metal body of the geyser is connected by a separate green wire to a copper plate buried outside.
1. Calculate the total current drawn when everything is on, explain why the fuse blew, and identify the least disruptive change that would keep the household within the 20 A limit.
Read the worked answer
Total connected load:
2000 + 1500 + 750 + 200 + (4 × 40 = 160) + 80 + 100 = 4790 W
Current I = P/V = 4790/220 = 21.8 A.
This exceeds the 20 A fuse rating, so the fuse element heated up and melted - exactly as designed. The fusing element is chosen to melt just above the maximum current the installation is meant to carry.
A fuse does not blow instantly at 20.1 A; it has a time–current characteristic, which is why the lights survived about ten minutes before the sustained overload melted the wire.
Least disruptive change: switch off the 1500 W heater. The load falls to 4790 − 1500 = 3290 W, giving 3290/220 = 15.0 A, comfortably within 20 A. Switching off the geyser instead gives 2790 W, or 12.7 A. The heater alone draws 6.8 A, so running it with the geyser and iron together is the combination that must be avoided.
Note also that the fuse protects the wiring, not the appliances; the correct response to a blown fuse is to reduce load or repair a fault, never to increase the rating.
2. Evaluate the neighbour's two suggestions and explain the purpose of the green earth wire on the geyser.
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Both suggestions are dangerous.
- Thick copper wire across the fuse terminals removes the protection completely. The wire will carry 21.8 A and far more without melting, so the circuit is unprotected. The current-carrying capacity of the house wiring is only slightly above 20 A; sustained overload heats the conductors, the PVC insulation softens, chars and finally ignites. A short circuit would then draw hundreds of amperes with nothing to interrupt it.
- A 30 A fuse is only marginally better. The overload that already occurred (21.8 A) would never trip it, so the cables would run hot continuously and the fire risk simply accumulates silently until a fault occurs.
A fuse must be rated just above the maximum normal current of the circuit and no higher than the safe current of the cable - never sized to match the appliances.
Earth wire: the metal body of a geyser is normally at earth potential. If a live wire inside touches the body, the body becomes live at 220 V. The green wire provides a low-resistance path to the buried copper plate, so a large current flows to earth and immediately blows the fuse or trips the MCB, cutting the supply. Without earthing, the body stays live and a person touching it and a tap forms the only path to earth - a potentially fatal shock. The earth wire must never be fused or disconnected.
3. The geyser runs for 1.5 hours a day. Calculate the monthly energy consumption and cost at ₹6.00 per unit, then judge whether a solar water heater costing ₹18,000 is worth installing.
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Monthly energy:
Power = 2000 W = 2 kW; daily energy = 2 kW × 1.5 h = 3 kWh (3 units). Monthly = 3 × 30 = 90 kWh; cost = 90 × ₹6.00 = ₹540 per month, i.e. ₹6,480 per year if used every day.
Solar judgement: the saving depends on how many days the sun actually does the job. In a region with about 250 usable sunny days, the solar heater would displace 250 × 3 kWh = 750 kWh, worth 750 × ₹6 = ₹4,500 per year. Payback ≈ 18,000/4,500 ≈ 4 years, after which the hot water is effectively free - a sound choice if the roof is unshaded and has a south-facing exposure, with a modest maintenance cost for the tank and pipes.
If, however, the geyser is used only in the four winter months (about 120 days), savings are 120 × 3 × ₹6 = ₹2,160 per year and payback stretches to about 8.3 years, which is far less attractive. The decision therefore needs actual usage data, not just the purchase price. In either case the solar route also cuts the evening load on the fuse, easing the overload problem directly.