Capacitors and Resistors in Parallel The capacitor in the figure is initially uncharged when the switch S is closed. Immediately after the switch is closed, the potential is the same at points c and d. + + + + - + - - +

Capacitors and Resistors in Parallel After some time, the capacitor is fully charged. + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - -

Capacitors and Resistors in Parallel After some time, the capacitor is fully charged. Switch is now re-opened. + + + + + + + + + + + + - - - - - - - - - - - -

An uncharged capacitor does not resist the flow of current and acts like a wire. No current flows thru the 8 Ω resistor; the capacitor acts as a short circuit between points c and d. Apply Kirchhoff’s loop rule to the outer loop abcdefa: 12 V – 4 Ω·I0 = 0; I0 = 3 A

12 V – 4 Ω·If – 8 Ω·If = 0; 12 V – 12 Ω·If; If = 1 A After the capacitor is fully charged, no more charge flows onto or off of the plates; the capacitor acts like a broken wire or open in the circuit. Apply Kirchhoff’s loop rule to loop abefa: 12 V – 4 Ω·If – 8 Ω·If = 0; 12 V – 12 Ω·If; If = 1 A

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Immediately Long time A1 ___________ V1 ___________ A2 ___________ Charge ______ V4 ___________ A1 ___________ V1 ___________ A2 ___________ V2 ___________ A3 ___________ V3 ___________ Charge ______ V4 ___________ 8 Amps 8 Volts 6 Amps 6 Volts 4 Amps 4 Volts 0 Amps 0 Volts Immediately Long time 4 Amps 4 Volts 6 Amps 6 Volts 0 Coulombs 0 Coulombs 0 Coulombs 6 Coulombs A3 A1 A2 V1 V2 V4 V3 12 V Charge = ? ? ?

Immediately Long time 6.0 μF 4.0 Ω 3.0 Ω 2.0 Ω 4.0 μF 1.5 μF V1 ___________ A2 ___________ V2 ___________ A3 ___________ V3 ___________ Charge1 _______ V4 ___________ Charge2 _______ V5 __________ V6 ___________ Charge3 _______ A1 ___________ V1 ___________ A2 ___________ V2 ___________ A3 ___________ V3 ___________ Charge1 _______ V4 ___________ Charge2 _______ V5 __________ V6 ___________ Charge3 _______ 2.31Amps 9.23 Volts 0 Amps 0 Volts 1.39 Amps 2.77 Volts 0 Amps 0 Volts 0.923 Amps 2.77 Volts 0 Amps 0 Volts Immediately Long time 0 Coulombs 0 Volts 18 μC 12 Volts 0 Coulombs 0 Volts 28.8 μC 7.2 Volts 0 Coulombs 0 Volts 28.8 μC 4.8 Volts A3 A1 V1 V2 V3 12 V A2 V4 6.0 μF V6 4.0 Ω 3.0 Ω 2.0 Ω V5 4.0 μF Charge2 Charge1 Charge3 1.5 μF