The Extension Board That Keeps Blowing Fuses
Rohit's study table has a single 5 A wall socket supplying 220 V. His extension board has a flex rated for 6 A and a 5 A fuse in the live wire. The appliances are an electric heater marked 1000 W, an electric iron marked 750 W, a 60 W table lamp and a 10 W phone charger. On a cold evening he switches on the heater and the iron together and the fuse blows after a few minutes. The same heater, run with the lamp, works all evening without trouble. A friend measures the heater element with a multimeter while the heater is cold and gets 42 ohm, whereas the marked power implies 48.4 ohm at working temperature. The landlord, tired of replacing fuses, suggests fitting a 15 A fuse in the board. Rohit wants to know which combinations he can safely run, why the fuse survived the first few minutes, and whether the landlord's suggestion is acceptable.
1. Calculate the current drawn by each appliance at 220 V. Which combinations can be run on the 5 A fuse, and why is the fuse placed in the live wire rather than the neutral?
Read the worked answer
Using I = P/V:
- Heater, 1000 W: I = 4.55 A
- Iron, 750 W: I = 3.41 A
- Lamp, 60 W: I = 0.27 A
- Charger, 10 W: I = 0.045 A
Safe on a 5 A fuse: heater alone (4.55 A), heater + lamp (4.82 A), iron + lamp + charger (3.73 A), lamp + charger alone. Not safe: heater + iron = 7.95 A, and this also exceeds the 6 A rating of the flex, so the flex itself is overloaded even before the fuse acts.
The fuse belongs in the live wire so that when it melts, the appliance is cut off from the high-potential line. If it were in the neutral, the fuse would still blow and stop the current, but the appliance would remain connected to the live wire; anyone touching an exposed part while standing on the floor would provide a path to earth and receive a shock, and the fuse would give no protection at all.
2. Why does the cold element read 42 ohm instead of 48.4 ohm, and what does this imply for the current at the instant of switching on? Use this to explain why the fuse did not blow the moment the heater was switched on.
Read the worked answer
The element is a metal alloy with a positive temperature coefficient of resistance. At room temperature it has fewer lattice vibrations to scatter conduction electrons, so its resistance is lower; at working temperature (several hundred degrees Celsius) it is higher. The 48.4 ohm value comes from R = V^2/P = 220^2/1000 and corresponds to the hot element, not the cold one.
At switch-on, I = 220/42 = 5.24 A, about 15% above the steady 4.55 A. This surge lasts only while the element heats, typically a fraction of a second to a few seconds. A fuse is a thermal device: the element must absorb enough energy to reach its melting point, so a modest overload sustained for a short time will not melt it. The 5 A fuse is designed to carry 5 A indefinitely and to blow only on a sustained overload, which is exactly what happened when the iron was added: the current rose to 7.95 A and stayed there, so the fuse heated and melted after a few minutes.
3. Evaluate the landlord's proposal to fit a 15 A fuse. What is the correct solution?
Read the worked answer
The proposal is dangerous and must be rejected. A fuse protects the wiring of the circuit, not the appliance. The flex of the board is rated 6 A; with heater and iron running it carries about 7.95 A, roughly 33% over its rating. The heat produced in a wire is I^2R, so the flex would run hotter than its insulation is designed for, the insulation would soften, char and could ignite, while the 15 A fuse would sit there quite happily because 7.95 A is well within its rating. The wall socket and the circuit cable behind it are also 5 A rated, so they too would be unprotected.
The correct actions: never run the heater and the iron together; run one heavy appliance at a time, ideally with nothing else on the board. If both must run, get a separate 15 A circuit with correctly rated cable and socket, or a board with a proper 6 A flex and separate switched sockets. Replacing the fuse with a thicker one removes the only protection in the chain and converts an inconvenience into a fire risk.