PhysicsLAB: 2006 C2 E&M

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.