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Capacitor X (2 uF) is charged to 120 V and capacitor Y (3 uF) is…
Question
Capacitor X (2 uF) is charged to 120 V and capacitor Y (3 uF) is charged to 30 V. They are then connected together so that the positively charged plate of one is joined to the negatively charged plate of the other (unlike-charge connection). Find the energy, in microjoules, dissipated as the system reaches its final common state.
✓ Verified answer: 13500checked by our engine — not a guess
Step-by-step solution
Initial charges: Q1 = 2*120 = 240 uC, Q2 = 3*30 = 90 uC.
With unlike plates joined, the net charge that must redistribute is Q1 - Q2 = 150 uC over total capacitance C1 + C2 = 5 uF, so the common voltage is V_c = 150/5 = 30 V.
Initial stored energy = 0.5*2*120^2 + 0.5*3*30^2 = 14400 + 1350 = 15750 uJ.
Final stored energy = 0.5*5*30^2 = 2250 uJ.
Energy dissipated = 15750 - 2250 = 13500 uJ.
Final answer13500
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