Final answer:
A damaged wire can result in increased resistance, leading to excessive heat and potential thermal hazards as the current flows through it. Fuses may fail to protect the circuit if they are not designed for this higher resistance, leading to overheating and safety risks.
Step-by-step explanation:
A damaged or nicked wire is a safety hazard because it can lead to overheating and potential fires. When a wire is damaged, its effective resistance can increase, causing excessive heat generation as current flows through it. This occurs because the power dissipated in the wire, described by the formula P = I²Rw, increases with higher resistance (Rw). If a damaged wire's resistance were to increase significantly, the power dissipated as heat could be much higher than the wire can safely handle, which may not be adequately protected by a fuse or circuit breaker designed for a lower resistance.
Fuses and circuit breakers are crucial for safeguarding electrical systems by interrupting the flow of current when it exceeds safe levels. In conditions where the wire resistance is larger than expected, as with a worn cord, the power loss (IR drop) can be significant. This is not only a concern for efficiency but also for safety as overheated wires can lead to thermal hazards.