AP Free Response Question
2003 C2 E&M
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In the laboratory, you connect a resistor and a capacitor with unknown values in series with a battery of emf = 12 V. You include a switch in the circuit. When the switch is closed at time t = 0, the circuit is completed, and you measure the current through the resistor as a function of time as plotted below.
A data-fitting program finds that the current decays according to the equation
(a) Using common symbols for the battery, the resistor, the capacitor, and the switch, draw the circuit that you constructed. Show the circuit before the switch is closed and include whatever other devices you need to measure the current through the resistor to obtain the above plot. Label each component in your diagram.
(b) Having obtained the curve shown above, determine the value of the resistor that you placed in this circuit.
(c) What capacitance did you insert in the circuit to give the result above?
You are now asked to reconnect the circuit with a new switch in such a way as to charge and discharge the capacitor. When the switch in the circuit is in position A, the capacitor is charging; and when the switch is in position B, the capacitor is discharging, as represented by the graph below of voltage V across the capacitor as a function of time.
(d) Draw a schematic diagram of the RC circuit that you constructed that would produce the graph above. Clearly indicate switch positions A and B on your circuit diagram and include whatever other devices you need to measure the voltage across the capacitor to obtain the above plot. Label each component in your diagram.
Topic Formulas
Description
Published Formula
Ampere's Law
Biot-Savat Law
capacitance
capacitance (dielectric)
capacitors in parallel
capacitors in series
Coulomb's Law
current density
electric current
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 current-carrying wire
Gauss' Law
induced emf (inductor)
induced emf (magnetism)
Joule's Law
magnetic field around a current-carrying 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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Parallel and Series Circuits
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Ampere's Law
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An Introduction to DC Circuits
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Capacitors and Dielectrics
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Dielectrics: Beyond the Fundamentals
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Electric Field Strength vs Electric Potential
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Electricity and Magnetism Background
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Filaments
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Inductors
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Kirchhoff's Laws: Analyzing Circuits with Two or More Batteries
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Kirchhoff's Laws: Analyzing DC Circuits with Capacitors
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LC Circuit
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Magnetism: Current-Carrying Wires
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Maxwell's Equations
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Meters: Current-Carrying Coils
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Parallel Plate Capacitors
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RC Time Constants
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RL Circuits
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Spherical, Parallel Plate, and Cylindrical Capacitors
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Torque on a Current-Carrying Loop
Worksheet:
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The Circuit Rider
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The Cycle Shop
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DC Currents
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Electric Power
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Ohm's Law
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Parallel Circuits
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Power Production
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Power Transmission
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RIVP Charts #1
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RIVP Charts #2
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Series Circuits
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Brightness
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Light and Heat
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Parallel Circuit
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Series Circuits
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Shock!
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Capacitors - Connected/Disconnected Batteries
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Combinations of Capacitors
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Induced emf
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Introduction to R | I | V | P Charts
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Kirchhoff's Laws: DC Circuits with Capacitors
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Kirchhoff's Laws: Sample Circuit
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Resistance, Wattage, and Brightness
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34A: Electric Current
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35A: Series and Parallel
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Advanced Capacitors
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Basic Capacitors
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Basic DC Circuits
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Electric Field Strength vs Electric Potential
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Multiple-Battery Circuits
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Textbook Set #6: Circuits with Multiple Batteries
CB-ETS
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