Question

1. (50pts.) Consider the circuit shown in the figure with R1 = R and R2 = R3 = 2R. The capacitor is initially uncharged and the switch S is suddenly closed. (a) (20pts.) Using Kirchhoff's rules, find the current through each of the resistors as a function of R and ?, just after the switch is closed. Make sure to indicate the loops you are using and the direction of the currents in a circuit diagram. (b) (15pts.) What is the potential difference across each of the resistors after a long time has passed and the capacitor is fully charged? Your answer should be expressed in terms of ?, the emf of the power supply. (c) (10pts.) Find the final charge on the capacitor as a function of ? and C. (d) (5pts.) Which end of the capacitor is positively charged and which one is negatively charged? Explain. (e) (Bonus 6pts.) If the switch S is re-opened once the capacitor is fully charged, write Q(t), the charge on the capacitor as a function of time, taking t = 0 to be the re-opening time. Your answer should be given in terms of ?, R, C, and naturally t. (f) (Bonus 6pts.) How much time does it take for the charge on the capacitor to decay to one third of its original value?

          1. (50pts.) Consider the circuit shown in the figure with R1 = R and R2 = R3 = 2R. The capacitor is initially uncharged and the switch S is suddenly closed.

(a) (20pts.) Using Kirchhoff's rules, find the current through each of the resistors as a function of R and ?, just after the switch is closed. Make sure to indicate the loops you are using and the direction of the currents in a circuit diagram.
(b) (15pts.) What is the potential difference across each of the resistors after a long time has passed and the capacitor is fully charged? Your answer should be expressed in terms of ?, the emf of the power supply.
(c) (10pts.) Find the final charge on the capacitor as a function of ? and C.
(d) (5pts.) Which end of the capacitor is positively charged and which one is negatively charged? Explain.
(e) (Bonus 6pts.) If the switch S is re-opened once the capacitor is fully charged, write Q(t), the charge on the capacitor as a function of time, taking t = 0 to be the re-opening time. Your answer should be given in terms of ?, R, C, and naturally t.
(f) (Bonus 6pts.) How much time does it take for the charge on the capacitor to decay to one third of its original value?

1. (50pts.) Consider the circuit shown in the figure with R1 = R and R2 = R3 = 2R. The capacitor is initially uncharged and the switch S is suddenly closed.

(a) (20pts.) Using Kirchhoff's rules, find the current through each of the resistors as a function of R and ?, just after the switch is closed. Make sure to indicate the loops you are using and the direction of the currents in a circuit diagram.
(b) (15pts.) What is the potential difference across each of the resistors after a long time has passed and the capacitor is fully charged? Your answer should be expressed in terms of ?, the emf of the power supply.
(c) (10pts.) Find the final charge on the capacitor as a function of ? and C.
(d) (5pts.) Which end of the capacitor is positively charged and which one is negatively charged? Explain.
(e) (Bonus 6pts.) If the switch S is re-opened once the capacitor is fully charged, write Q(t), the charge on the capacitor as a function of time, taking t = 0 to be the re-opening time. Your answer should be given in terms of ?, R, C, and naturally t.
(f) (Bonus 6pts.) How much time does it take for the charge on the capacitor to decay to one third of its original value?

Added by Michael M.

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