Final answer:
The statement is false. Resistors are designed to dissipate heat, but excessive current can cause them to overheat and potentially fail. Ohm's law is not violated by the resistor getting hot.
Step-by-step explanation:
The statement that under proper operating conditions, a resistor should never get hot enough to be hot to the touch is false. While it is true that a resistor is designed to dissipate power in the form of heat, under normal conditions this should not lead to the resistor getting excessively hot. However, if an excessive amount of current flows through a resistor, it can indeed become hot to the touch. The heat generated in a resistor is given by the power, which is the product of the voltage across the resistor and the current flowing through it (P = IV). Therefore, if either the voltage is high or the current is too large, the power dissipated will increase and the resistor may overheat. This overheating can lead to a change in the resistor's state, potentially damaging it or causing failure. Ohm's law, which describes the relationship between voltage, current, and resistance (V = IR), is not violated by the heating of the resistor but rather by the parameters exceeding design specifications.
Fuses are often added to circuits to prevent accidents that can be caused by overheating resistors due to excessive current. It is important to note that while a resistor can handle small increases in temperature, if it gets too hot, it can fail and potentially affect the entire circuit.