PhysicsLAB AP Free Response Question
2006 C2 E&M

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The circuit below contains a capacitor of capacitance C, a power supply of emf , two resistors of resistances R1 and R2, and two switches, S1 and S2.
Initially, the capacitor is uncharged and both switches are open. Switch S1 then gets closed at time t = 0.
 (a) Write a differential equation that can be solved to obtain the charge on the capacitor as a function of time t.

 (b) Solve the differential equation in part (a) to determine the charge on the capacitor as a function of time t.

Numerical values for the components are given as follows:

 = 12 V
C  = 0.060 F
R1 = R2 = 4700
 (c) Determine the time at which the capacitor has a voltage 4.0 V across it.

After switch S1 has been closed for a long time, switch S2 gets closed at a new time t = 0.
(d) On the axes below, sketch graphs of the current I1 in R1 versus time and of the current I2 in R2 versus time, beginning when switch S2 is closed at new time t = 0. Clearly label which graph is I1 and which is I2.

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