1. 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. + + + + - + - - +

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

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

4. 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

5. 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

6. + + -

8. 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 = ? ? ?

9. 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