F capacitor c 2 after the switch is closed charge

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F capacitor (C 2 ). After the switch is closed, charge flows from C 1 to C 2 until an equilibrium is established with both capacitors at the same potential difference, Δ V f . What energy is stored in the two capacitors after the switch has been closed? Answer Usually no coordinate system needs to be defined for a capacitor (start with the original charge amount Q o .)
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Capacitance Answer The original charge, Q o , shared by the two capacitors is: Next, turn to the definition of capacitance: Q o = Q 1 + Q 2 Substituting back into our charge equation gives us: But we know the final potential difference is the same between the two capacitors: Δ V 1 = Δ V 2 = Δ V f C 1 Δ V o ( ) = C 1 Δ V 1 ( ) + C 2 Δ V 2 ( ) C 1 Δ V o ( ) = C 1 Δ V f ( ) + C 2 Δ V f ( ) = C 1 + C 2 ( ) Δ V f
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Capacitance Answer Solving for Δ V f gives us: Putting this common potential difference into the energy equation gives us: Δ V f = C 1 Δ V o ( ) C 1 + C 2 ( ) Δ V f = 3.55 μ F 6.30V ( ) 3.55 μ F + 8.95 μ F ( ) = 1.79V E Tot = E 1 + E 2 E Tot = 1 2 C 1 Δ V f ( ) 2 + 1 2 C 2 Δ V f ( ) 2 E Tot = 1 2 C 1 + C 2 ( ) Δ V f ( ) 2 E Tot = 1 2 3.55 μ F + 8.95 μ F ( ) 1.79V ( ) 2 = 20.0 μ J
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For Next Time (FNT) Start reading Chapter 26 Keep working on the homework for Chapter 25
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