Final answer:
Jane's electrical extension cord is likely getting hotter because it's overloaded with too great a current, leading to higher power dissipation due to increased resistance or wear and tear.
Step-by-step explanation:
Jane observed her electrical extension cord was heating up as she worked with her electrical device. This heating is likely due to an overloaded cord where the current (I) flowing through it is too great, causing an increase in power dissipation (P), which is described by the formula P = I²Rw, where R is the resistance of the wire (Rw). An inexpensive extension cord often has a higher resistance than a heavier-duty one, thus it can generate more heat.
Moreover, a hot cord can indicate that the wire's resistance (Rw) may have changed over time due to wear and tear, potentially increasing from something like 0.100 ohms to 2.00 ohms. This would drastically increase the power dissipated by the cord, causing it to overheat. Furthermore, this correlates with the concept that if a cord originally designed to carry a small current, say a few amps, ends up carrying a much larger current, the power dissipation can increase significantly to levels that are unsafe, such as 1000 W, leading to thermal hazards.
Safe practices, like using a cord of the correct gauge and ensuring that fuses and circuit breakers are in place to protect against excessive current flows, are important to prevent overheating of extension cords. In summary, the heat observed by Jane in her extension cord is most likely a result of an overloaded and potentially worn cord with increased resistance.