Extension Lead Overload and Fuse Protection
A householder connects a 2.5 kW electric heater and a 1.2 kW kettle to a single four-way extension lead. The lead is fitted with a 13 A fuse and its cable is marked 1.0 mm², which has a current rating of 10 A. The wall socket is protected by a 32 A circuit breaker. The mains voltage is 230 V. The extension lead is coiled loosely but not fully unwound. After several minutes, the lead feels warm and the plug becomes hot. The heater and kettle are both resistive and are used at the same time. The cable resistance is 0.020 Ω per metre and the lead is 5 m long. The householder says the 13 A fuse will protect the cable because 13 A is more than 10 A, so it will blow before the cable overheats.
1. Calculate the total current and assess whether the fuse protects the cable in this situation.
Read the worked answer
Total power = 2.5 kW + 1.2 kW = 3.7 kW = 3700 W. For resistive loads the current is:
I = P/V = 3700/230 = 16.1 A.
This exceeds both the cable rating of 10 A and the 13 A fuse rating. The fuse is not a precise current limiter: a 13 A fuse may carry 16 A for a considerable time without blowing, and it is intended mainly to protect the flexible cord against fault currents. It does not guarantee that a 16 A overload is disconnected quickly. The householder's reasoning is therefore unsafe: the cable can overheat before the fuse operates.
2. Calculate the power dissipated in the lead and explain why the cable and plug become warm.
Read the worked answer
The lead is 5 m long, but there are two conductors carrying current (live and neutral), so the total length of conducting cable is about 10 m. Resistance:
R = 0.020 × 10 = 0.20 Ω.
Power dissipated:
P = I²R = (16.1)² × 0.20 = 52 W.
This heat is produced along the cable. Because the lead is coiled, heat is trapped and the cable temperature rises. The plug also becomes warm because of contact resistance at the pins and socket, which adds to the heating. The cable is outside its 10 A rating, so its insulation may degrade.
3. Recommend a safer arrangement and explain why the 32 A circuit breaker does not solve the problem.
Read the worked answer
The heater and kettle should be plugged into separate wall sockets, or used one at a time. If an extension lead is essential, it should be fully unwound and have a cable rating of at least 16 A, with a fuse appropriate to that cable.
The 32 A circuit breaker protects the fixed installation wiring, not the extension lead; it will not trip at 16 A. The 13 A fuse does not make a 10 A cable safe. The correct principle is that the fuse or breaker must be rated at or below the cable's current-carrying capacity, and the load must be kept within that rating.