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AP Physics C: E & M

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Unit 2

2.2 Capacitors ๐Ÿ“ธ

2 min readโ€ขnovember 3, 2020

peter57616

Peter Apps


What's a Capacitor?

A capacitor is a device that can be used to store charge, and therefore, electrical potential energy. They are used in a wide range of electrical devices including the flash on your cell phone camera. There are several different ways to construct a capacitor, but we're going to focus on the parallel-plate version.
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Image from Wikipedia

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Image from Wikipedia

The parallel plate capacitor is created by taking two conductive plates and separating them by a small distance. A dielectric is often added to increase the amount of charge a capacitor can store. We'll discuss more about dielectrics in the next section.

Theory Time - Parallel Plate Capacitor ๐ŸŽ“

Let's create a simple capacitor using two metal plates and connect them to a battery to charge them up. Recall from Unit 1, that the strength of the electric field is proportional to the amount charge.
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Image from opentextbc.ca

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This equation is for a capacitor where the plates are separated by air. We're going to tweak this equation a bit in the dielectric section when we discuss different materials to place between the plates.
From here, we can see that capacitance is directly proportional to the area of the plates (A) and inversely proportional to the distance between them. This should make sense since a larger plate has more room for the charge to occupy and, therefore, more should be able to fit on it.

Other Types of Capacitors

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Image from Wikipedia.org

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Image from toppr.com

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Energy in a Capacitor ๐Ÿ’ก

Because the capacitor stores charge, it also stores electric potential energy (Uc). The amount of energy stored can be determined through the following derivation. We're going to imagine moving a tiny bit of charge (dq) from one side of the capacitor to the other. The charge will gain energy that's proportional to the potential difference passed through.
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Take a few minutes and check out this Phet Simulation where you can alter the physical properties of a parallel plate capacitor and see the effect on voltage, field strength and energy stored

Practice Questions ๐Ÿ‘

  1. A 20 ยตF parallel-plate capacitor is fully charged to 20 V. The energy stored in the capacitor is most nearly __________.
    • Answer:
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  2. A capacitor with circular parallel plates of radius R that are separated by a distance d has a capacitance of C. What would the capacitance (in terms of C ) be if the plates had radius 2R and were separated by a distance d/2?
    • Answer:
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  3. Image below
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    • Answer:
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