A worn appliance cord has a resistance of 2.00 ohm instead of the 0.100 ohm it should have. What power is dissipated in it when 10.0 A flows?
A200 W
B20.0 W
C100 W
D400 W
Answer & Solution
Correct answer: A. 200 W
1. For supply wires the loss is P = I squared R_w, with R_w the resistance of the wires themselves.
2. Square the current: (10.0 A) squared = 100 A squared.
3. Multiply by the worn resistance: P = (100 A squared)(2.00 ohm) = 200 W.
4. A healthy cord at 0.100 ohm would dissipate only 10.0 W at the same current.
5. Twenty times the heat inside insulation designed for 10 W is far more than is safe.
6. 20.0 W is the trap of using P = I R rather than P = I squared R.
7. 400 W would follow from doubling the current before squaring it.
_Source: OpenStax College Physics (CC BY 4.0), Ch 20 "Electric Current, Resistance, and Ohm's Law", section Thermal Hazards_
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