What describes the heat developed by a resistor carrying a steady current over time?

• A. It increases linearly
• B. It decreases over time
• C. It remains constant
• D. It exponentially decreases

Answer: (A)

The heat developed by a resistor carrying a steady current over time is best described as increasing linearly. When a current passes through a resistor, it generates heat as a result of electrical resistance, following Joule's law, which states that the power (P) dissipated as heat in a resistor is proportional to the square of the current (I) times the resistance (R): P = I²R.

Since the current is steady, the power remains constant, leading to a consistent rate of heat generation. When you consider the heat produced over a certain duration, heat accumulates in a linear fashion with respect to time, meaning that if you observe the system over a longer period, the total heat generated will be directly proportional to that time, assuming no other heat loss mechanisms are significantly affecting the system.

This understanding is pivotal when analyzing circuits and thermal management in electrical systems, as it indicates that as time progresses, the total heat rises consistently as long as the current remains steady.