Fuse Rating in a Winter Load
A rented house in Muzaffarpur has one 230 V circuit protected by a 5 A fuse. The connected appliances are three LED lamps of 9 W each, two ceiling fans of 75 W each, one television of 80 W, one refrigerator of 180 W, and a 1500 W immersion rod used on winter mornings. The wiring is old, with 1.0 mm² copper conductors; the meter is rated 10 A. One cold morning, with the refrigerator compressor already running, the family switches on the immersion rod and all the lights. The fuse melts within seconds. The landlord's electrician says the simplest fix is to replace the fuse wire with a thicker aluminium wire or to fit a 15 A fuse, because 'the appliances are fine and the fuse is simply too weak'. The family wants hot water daily and does not want repeated power cuts, but they also cannot afford a complete rewiring of the house.
1. Calculate the total current when every listed appliance runs at once. Is the 5 A fuse adequate? Recommend a fuse rating and state one condition that must accompany your recommendation.
Read the worked answer
Add the powers: lamps 3 × 9 = 27 W; fans 2 × 75 = 150 W; television 80 W; refrigerator 180 W; immersion rod 1500 W. Total = 27 + 150 + 80 + 180 + 1500 = 1937 W.
For a resistive load, I = P/V = 1937/230 ≈ 8.4 A. The 5 A fuse can carry only about 5 × 230 = 1150 W, so it is not adequate; it melts because the actual current is about 8.4 A, well above its rating.
A 10 A fuse (or 10 A MCB) is the smallest standard rating above 8.4 A. But the immersion rod alone takes 1500/230 ≈ 6.5 A, and the refrigerator surge may add a short high pulse. The safe recommendation is a 10 A fuse for the lighting/fan/television/refrigerator circuit, plus a separate 16 A circuit with 2.5 mm² copper wire for the immersion rod. Simply fitting a larger fuse without separating the heavy load is not safe.
2. Evaluate the electrician's two suggestions: replacing the fuse wire with thicker aluminium wire, or fitting a 15 A fuse. Use the 1.0 mm² wiring in your answer and state what should actually be done.
Read the worked answer
Both suggestions defeat the purpose of the fuse. A fuse is the deliberately weak link that melts before the wiring overheats.
A 15 A fuse permits up to 15 × 230 = 3450 W. The 1.0 mm² copper conductors in the house are typically rated for only about 10–11 A, so a 15 A fuse could allow the wiring to overheat and start a fire before the fuse acts.
A thicker aluminium wire is worse: aluminium has higher resistivity than copper for the same size, and its oxide layer increases contact resistance at terminals. It may carry more current than the old fuse, but it will not melt at the intended current, so the household wiring becomes the weakest part of the circuit.
Correct action: fit a 10 A fuse or MCB, check the earthing, and give the 1500 W immersion rod its own 16 A circuit with proper 2.5 mm² copper wiring. If rewiring is impossible immediately, the immersion rod should not be run together with all other appliances.
3. Explain, in terms of the refrigerator motor, why the fuse is more likely to melt at the instant the compressor starts than after it has been running steadily.
Read the worked answer
A motor draws a large starting current because when the rotor is stationary there is no back emf. The current is limited mainly by the low resistance of the winding, so it can be several times the normal running current.
As the motor speeds up, the changing magnetic flux induces a back emf that opposes the supply voltage. The net voltage across the winding falls, so the current drops to its normal running value.
The fuse melts according to heating proportional to I²t. A short starting surge is usually tolerated, but if the circuit is already loaded near 8.4 A, the extra surge at compressor start can push the total above the 5 A fuse rating long enough to melt it. After the compressor has run for a few seconds, the current falls and the fuse is less likely to blow.