Three equal capacitors P, Q and S, each C, are connected across a battery of voltage V. P and Q form the upper series branch, while S is a single capacitor in parallel with that branch. Find Uₚ/Uₜ, where Uₚ is the energy stored in P and Uₜ is the total stored energy. Image
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Question

Three equal capacitors P, Q and S, each C, are connected across a battery of voltage V. P and Q form the upper series branch, while S is a single capacitor in parallel with that branch. Find Uₚ/Uₜ, where Uₚ is the energy stored in P and Uₜ is the total stored energy. Image

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G1 Physics · Accepted Answer

Step 1: P and Q in series have equivalent capacitance C/2; the series branch has the full battery voltage V. Step 2: Each series capacitor therefore has voltage V/2. Energy in P is Uₚ = (1/2)C(V/2)² = CV²/8. Step 3: Total equivalent capacitance is C/2 + C = 3C/2. Step 4: Total energy Uₜ = (1/2)(3C/2)V² = 3CV²/4. Step 5: Ratio Uₚ/Uₜ = (CV²/8)/(3CV²/4) = 1/6. Final answer: 1/6 (Option D).