Extension Cord on a Reel: A 15 A Breaker and a 10 A Cord
A student sets up a demonstration in the school gym: a 1500 W electric kettle rated at 120 V is plugged into a 25 m, 16 AWG extension cord (about 0.013 ohms per metre of conductor) that is still wound on its plastic reel. The branch circuit is protected by a 15 A circuit breaker. The cord jacket is marked 10 A. The building wiring in the wall is 14 AWG, which is what the 15 A breaker is there to protect. After ten minutes on a previous run the reel felt hot to the touch and the kettle took noticeably longer to boil than it does in the kitchen. A teacher suggests swapping in a 20 A breaker so the circuit 'stops being marginal.' Assume the kettle element keeps a constant resistance of 9.6 ohms and the supply is exactly 120 V.
1. Compute the steady current, the voltage drop along the cord, the power dissipated in the cord, and the power delivered to the kettle. Then judge whether the arrangement is safe, and explain precisely what the 15 A breaker does and does not protect.
Read the worked answer
The cord carries current out along one conductor and back along the other, so the path length is 50 m: R_cord = 0.013 x 50 = 0.66 ohms. The series circuit is 9.6 + 0.66 = 10.26 ohms.
- Current: I = 120/10.26 = 11.7 A
- Cord voltage drop: 11.7 x 0.66 = 7.7 V, about 6.4% of the supply
- Power in the cord: I^2 R = 137 x 0.66 = 90 W, spread along 50 m of small conductor
- Power delivered: 137 x 9.6 = 1315 W, so the kettle runs 12% slow
The breaker sees 11.7 A against a 15 A threshold, so it never trips. That is not a malfunction. A branch breaker exists to protect the fixed wiring inside the wall, and 14 AWG is rated for 15 A; the breaker has no knowledge of what is plugged in downstream.
The cord is a separate problem. It is marked 10 A and is carrying 11.7 A, so it is running above its own rating and dissipating about 90 W in insulation that was never designed to shed it. Coiled on the reel, that heat has nowhere to go: the inner turns are wrapped in their own warm jacket. Insulation softens, resistance rises, dissipation rises again, and the failure runs away. This is the classic mechanism behind reel-and-cord fires, and the breaker is not in a position to stop it.
2. Evaluate three proposed fixes with numbers: replacing the cord with a 25 m 12 AWG cord (0.0052 ohms per metre of conductor), using a 1 m 16 AWG cord plugged directly into a nearby wall outlet, and installing the 20 A breaker.
Read the worked answer
12 AWG cord. R_cord = 0.0052 x 50 = 0.26 ohms; total 9.86 ohms; I = 12.2 A; drop = 3.2 V; cord dissipation = 148 x 0.26 = 38 W; kettle receives 1422 W. Current is slightly higher because the cord steals less voltage, but 12 AWG is rated for 20 A, so 12.2 A is comfortably inside its rating and the heat per metre falls by more than half. This is the correct fix, and a shorter heavy cord is even better.
1 m 16 AWG cord. R_cord = 0.026 ohms, so the drop is 0.3 V and cord dissipation is about 3.6 W. At that length the cord is doing its job; the hazard scales with length because the same small wire must carry current over a much longer resistance.
20 A breaker. This is the wrong change and makes things worse. The breaker would now allow 20 A through 14 AWG wall wiring rated at 15 A, so a genuine overload could heat the wall wiring without tripping anything. It also does nothing about the 10 A cord: the kettle draws 11.7 A, which trips neither breaker, so the cord keeps overheating exactly as before while the teacher believes the problem is solved. The proposal removes protection rather than adding it. Breakers are selected from the conductor they protect, not from the appliance's convenience.
3. Explain quantitatively why the kettle boils more slowly, and why the effect is somewhat larger than the steady-state power ratio alone suggests.
Read the worked answer
Energy to boil is fixed by the water mass and the starting temperature, so time scales inversely with power. The steady-state ratio is 1315/1500 = 0.88, predicting a boil time about 14% longer than on a direct outlet. That alone is the visible symptom the student noticed.
Two second-order effects push it slightly further. First, the element's resistance is given as constant here, but real nichrome elements have a positive temperature coefficient; when the element receives less voltage it runs cooler, its resistance drops slightly, and the current creeps up, which partially offsets the loss but changes the steady state away from the simple ratio. Second, the kettle is not the only load on the coil: the reel's stored heat raises the cord's resistance as it warms, increasing the drop as the run proceeds, so the element sees progressively less than 112 V.
The pedagogical point is that the cord is not a neutral wire. It is a resistor in series with the load, chosen by the appliance designer to be negligible over one metre and not over twenty-five. When it stops being negligible, the observable is a slower kettle, but the actual concern is the 90 W being deposited inside a plastic reel.