Final answer:
The power rating of a resistor is very important in a circuit to prevent damage. The change in resistance due to temperature is true but does not justify disregarding the power rating. The correct answer is A is false and R is true. Option number d is correct.
Step-by-step explanation:
The assertion (A) that the power rating of a resistor is not important when used in a circuit is incorrect. The power rating indicates the maximum power the resistor can safely dissipate without getting damaged. On the other hand, the reason (R) that the resistance value changes with temperature is true, as resistance does indeed vary with temperature based on the material's temperature coefficient of resistivity, given by the equation R = R₀ (1 + αΔT), where α is the temperature coefficient.
However, the change in resistance due to temperature is not the correct explanation for why power rating might be considered unimportant. The power rating is crucial as it ensures the resistor can handle the power without overheating or failing, irrespective of the change in resistance with temperature. Therefore, the correct answer is option (d): A is false and R is true.
Discussing the contradiction in the formulas for power dissipation in a resistor, P = V²/R implies power decreases with increasing resistance, while P = I²R shows power increases with increasing resistance. There is no contradiction because these formulas apply under different conditions: the former when voltage is constant and the latter when current is constant.