The plate areas and separations of five parallel-plate capacitors are: capacitor 1: area A₀, separation d₀; capacitor 2: area 2A₀, separation 2d₀; capacitor 3: area 2A₀, separation d₀/2; capacitor 4: area A₀/2, separation 2d₀; capacitor 5: area A₀, separation d₀/2. Rank their capacitances from least to greatest.
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Question

The plate areas and separations of five parallel-plate capacitors are: capacitor 1: area A₀, separation d₀; capacitor 2: area 2A₀, separation 2d₀; capacitor 3: area 2A₀, separation d₀/2; capacitor 4: area A₀/2, separation 2d₀; capacitor 5: area A₀, separation d₀/2. Rank their capacitances from least to greatest.

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G1 Physics · Accepted Answer

Use Q = CV, U = ½CV² and C = εA/d; reduce the capacitor network by series/parallel combination and apply charge conservation where a node is isolated. The result matches D (4, 1 and 2 tie; then 5, 3).