PhysicsLAB AP Free Response Question
2001 C2 E&M

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.

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