Household Circuit Overload and Broken Earthing
A room is wired to a 220 V supply through a 10 A fuse. The room contains a 1500 W electric heater, a 1000 W iron, and five 60 W lamps. All the appliances are switched on at the same time. The student living there says the 10 A fuse is unnecessary because the appliances are all separate and each has its own switch. Later, the metal body of the iron develops a fault and the student feels a shock when touching it, even though the fuse has not blown. The wiring is old and the earth connection in the socket is broken. The student wants to know why the fuse did not protect him and what current would have blown it. Assume the supply voltage stays at 220 V and the appliances obey Ohm's law.
1. Calculate the total current when all the appliances are on. Decide whether the 10 A fuse is adequate.
Read the worked answer
Total power = 1500+1000+5×60 = 2800 W. Current I = P/V = 2800/220 ≈ 12.7 A. This exceeds the 10 A fuse rating, so the fuse should blow. The appliances cannot all be run together on this circuit.
2. Suggest a safe way to operate the appliances on the 10 A circuit. Support your answer with current calculations for possible combinations.
Read the worked answer
On a 10 A, 220 V circuit the safe maximum power is 10×220 = 2200 W. Heater + five lamps = 1500+300 = 1800 W → I = 8.18 A (safe). Iron + five lamps = 1000+300 = 1300 W → I = 5.91 A (safe). Heater + iron = 2500 W → I = 11.36 A (unsafe). A safe arrangement is to run the heater and iron at different times, or put the heater on a separate circuit with a suitable fuse and wiring.
3. Explain why the broken earth connection allowed the shock and why the fuse did not blow.
Read the worked answer
The fault connects the live wire to the metal body. With the earth wire broken, the body is not forced to earth potential. When the student touches the iron, his body provides a path to earth, so a small current flows through him; this current is far below 10 A, so the fuse does not blow. A working earth wire would provide a low-resistance path, causing a large current that blows the fuse or trips the circuit. The fuse protects the wiring from overload; it does not by itself prevent shock from a faulty metal body.