Final answer:
No contradiction exists between the formulas P = V²/R and P = I²R for power dissipation in a resistor because Ohm's Law ties voltage, current, and resistance together. Changes in resistance impact current and voltage, explaining the power dissipation relationship according to which formula is in use. The correct option is d).
Step-by-step explanation:
Understanding the Power Dissipation in a Resistor
Electric power dissipation in a resistor can be expressed by two formulas: P = V²/R and P = I²R. At first glance, these equations seem contradictory because one suggests power decreases with increasing resistance, while the other suggests power increases. However, the key to understanding why there is no contradiction lies in Ohm's Law, which relates voltage (V), current (I), and resistance (R). According to Ohm's Law, V = IR. Therefore, if we substitute IR for V in the first equation, we get P = (IR)²/R which simplifies to P = I²R, matching the second equation. Conversely, substituting V/R for I in the second equation gives us P = (V²/R)R which simplifies to P = V²/R, aligning with the first expression.
The apparent discrepancy arises because we assume other variables remain constant while changing resistance. In reality, if you increase resistance, the current will decrease if the voltage remains constant (I = V/R), and similarly, if the voltage is constant, power dissipation will indeed decrease. However, if resistance increases while current remains constant, that necessitates an increase in voltage (V = IR), which would lead to an increase in power dissipation. Thus, both formulas are correct, and the correct option that explains this situation is (d) Ohm's Law explains the relationship.