Write the expressions for the energy stored in a capacitor. A capacitor C, charged to V, is joined to an identical uncharged capacitor. Find the common potential and the energy lost.
How to lay out the answer. Follow the frame, then write it in your own words.
1 · Write the formulae. U = Q²/(2C) = ½CV² = ½QV; energy density u = ½ε₀E².
2 · Common potential. Charge is conserved: CV = (C + C)V′, so V′ = V/2.
3 · Energy before. U₁ = ½CV².
4 · Energy after. U₂ = ½(2C)(V/2)² = ¼CV².
5 · Energy lost. U₁ − U₂ = ¼CV², half the original energy, given out as heat in the connecting wires.
6 · Real life. A defibrillator releases a capacitor's stored energy to restart a heart.
7 · Close in one line. Charge is conserved on sharing, but some energy is always lost as heat.
Scoring tip: Say where the lost energy goes (heat in the wires). A bare number without that line usually loses a mark.
