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
R
_{1}
and
R
_{2}
, and two switches,
S
_{1}
and
S
_{2}
.
Initially, the capacitor is uncharged and both switches are open. Switch S
_{1}
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
R
_{1}
= R
_{2}
= 4700
(c) Determine the time at which the capacitor has a voltage 4.0 V across it.
After switch S
_{1}
has been closed for a long time, switch S
_{2}
gets closed at a new time t = 0.
(d) On the axes below, sketch graphs of the current I
_{1}
in R
_{1}
versus time and of the current I
_{2}
in R
_{2}
versus time, beginning when switch S
_{2}
is closed at new time t = 0. Clearly label which graph is I
_{1}
and which is I
_{2}
.
Topic Formulas
Description
Published Formula
Ampere's Law
BiotSavat Law
capacitance
capacitance (dielectric)
capacitors in parallel
capacitors in series
Coulomb's Law
current density
electric current
electric field
electric field strength
electric potential energy
energy stored in a capacitor
energy stored in an inductor
Faraday's Law
force ona currentcarrying wire
Gauss' Law
induced emf (inductor)
induced emf (magnetism)
Joule's Law
magnetic field around a currentcarrying wire
magnetic field of a solenoid
magnetic flux
magnetic force on a moving charge
motional emf
Ohm's Law
potential due to a collection of point charges
resistance in parallel
resistance in series
resistivity
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