Final answer:
The power dissipation in a resistor is dependent on the circuit conditions. Power decreases with increasing resistance for a given voltage but increases with resistance for a given current. The context of the circuit (constant current or voltage) determines whether the resistor with the greatest or least resistance will dissipate the most power.
Step-by-step explanation:
The power dissipated by a resistor can indeed depend on its resistance, but to understand which resistor dissipates more power, we must consider the context of how it is connected in the circuit. It is not correct to say that power dissipation is directly proportional to resistance alone, nor that it is inversely proportional. The formula P = V2/R shows that for a given voltage, power dissipation decreases with increasing resistance. Conversely, the formula P = I2R indicates that, for a given current, power dissipation increases with resistance.
These two perspectives do not contradict because they apply in different situations. For a constant voltage scenario (like across a parallel branch in a circuit), the resistor with less resistance will dissipate more power because the current through it will be higher. In a constant current scenario (like in a series circuit), the resistor with more resistance will dissipate more power. So, the resistor that dissipates the most power depends on other factors beyond simply looking at resistance values.
Resistors generally dissipate power in the form of heat. The energy that is dissipated by the resistor in this way is lost to the surrounding environment, which typically increases the temperature of the resistor and the area immediately around it. In practical applications, the design has to consider how much heat a resistor will generate to ensure it doesn't damage the circuit or exceed its specified power rating.