A2 Daily A Level Physics question
A capacitor of capacitance C is charged to a potential difference V₀. It is then fully discharged through a resistor of resistance R. The same capacitor is then charged again to V₀ and fully discharged through a resistor of resistance 2R. Which statement correctly compares the total energy dissipated and the initial rate of energy dissipation in the second resistor compared to the first?
Answer
The correct answer is C.
The total energy stored in a capacitor is given by the formula E = ½CV₀². When the capacitor is fully discharged, all of this stored energy is dissipated as thermal energy in the resistor. Since the capacitance C and the initial potential difference V₀ are identical in both scenarios, the total energy dissipated in the resistor must also be the same. The rate of energy dissipation is power, P. At the instant the discharge begins (t=0), the potential difference across the resistor is V₀. Using the power formula P = V²/R, the initial power in the first case is P₁ = V₀²/R. In the second case, the resistance is 2R, so the initial power is P₂ = V₀²/(2R). By comparing the two, we see that P₂ = ½ P₁, meaning the initial rate of energy dissipation is halved.