AP Free Response Question
2001 C2 E&M
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You have been hired to determine the internal resistance of 8.0 µF capacitors for an electronic component manufacturer. (Ideal capacitors have an infinite resistance - that is, the materials between their plates is a perfect insulator. In practice, however, the material has a very small, but nonzero, conductivity.) You cannot simply connect the capacitors to an ohm-meter, because their resistance is too large for an ohm-meter to measure. Therefore you charge the capacitors to a potential difference of 10 V with a battery, disconnect it from the battery, and measure the potential difference across the capacitor every 20 minutes with an ideal voltmeter, obtaining the graph shown above.
(a) Determine the internal resistance of the capacitor.
The capacitor can be approximated as a parallel-plate capacitor separated by a 0.11 mm thick dielectric with κ = 5.6.
(b) Determine the approximate surface area of one of the capacitor "plates."
(c) Determine the resistivity of the dielectric.
(d) Determine the magnitude of the charge leaving the positive plate of the capacitor in the first 100 min.
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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Power Production
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Power Transmission
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Series Circuits
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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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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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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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