Final answer:
An undersized wire causes overheating due to the excessive power dissipation, which can lead to false alarms when the equipment's tolerance is exceeded, underscoring the need for proper wire sizing and safety devices like fuses and circuit breakers.
Step-by-step explanation:
Undersized wire that is supplying power to devices can cause false alarms due to the potential for overloading and overheating. When the electrical current (I) flowing through a wire exceeds the wire's capacity due to undersizing or wear, the power (P) dissipated as heat can be expressed by the equation P = I²Rw, where Rw is the wire's resistance. The combination of high current and increased resistance can lead to excessive power being dissipated as heat, causing the wire temperature to rise and potentially inducing false alarms from safety devices like smoke detectors. Suitable protections like fuses and circuit breakers are designed to interrupt the current flow and prevent these hazards by automatically opening the circuit when currents exceed safe thresholds.
Undersized wire that is supplying power to devices can cause false alarms. When wires supplying power to a user are overloaded with too great a current, the resistance of the wires (Rw) increases. As a result, the power dissipated in the wires (P) increases, leading to overheating. For example, if a wire with a resistance of 0.100 Ohms is meant to carry a few amps but is instead carrying 100 A, it will severely overheat and cause false alarms.
Fuses and circuit breakers are used to limit excessive currents. These components automatically open the circuit when a sustained current exceeds safe limits, preventing potential hazards such as false alarms.