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Chapter_5

# Chapter_5 - General Physics II Capacitors and Dielectrics...

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General Physics II Capacitors and Dielectrics The ideas of energy storage in E-fields can be carried a step further by understanding the concept of "Capacitance." Consider a sphere with a total charge, Q, and a radius, R. From previous problems we know that the potential at the surface is, Q Vk R = Putting more charge on the sphere stores more energy, but the ratio of energy or potential to charge depends only on R, not on Q or V. That is, 0 4 QR R πε == . It's true for all charged objects that the ratio of potential to voltage depends only on the shape, so this ratio is defined as the capacitance. Gaziantep University Faculty of Engineering Department of Engineering Physics 1 . The units of capacitance are 1 coulomb 1 Farad 1 F. volts ≡≡ Common values of capacitance are microfarads, µ F (10 -6 Farads) and picofarads, pF (10 -12 Farads). Q C V Consider two conductors connected to the terminals of a battery. The battery will supply an equal amount of charge, but of opposite sign, to each of the conductors. The question arising at this point: what will be capacitance of the conductor system? Let us consider different conductor systems: Parallel plates Two conducting parallel plates separated by a distance d with charges + Q and - Q . The potential difference between the plates (from one plate to the other) is s ab VVVE d oo Qd d A ρ ε = ⎛⎞ −== = ⎜⎟ ⎝⎠ . The capacitance is Conducting concentric spheres Two concentric spheres of radii R and r . The potential difference between the spheres is 11 4 o Q VVV R r −== . r R 4 o Q C V R r 0 A Q C Vd The capacitance is Coaxial Cable

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General Physics II Coaxial cable (two concentric conducting cylinders) of length L . The inside conductor has a radius r with charge ρ A and the inside surface of the outside conductor is R with charge - A . ln ab ln 22 oo R QR rL r VVV λ πε −== 3 = r R 2 ln o L Q C R V r == L The capacitance is Exercise There are electrical devices that are designed to store energy in this fashion. These devices are referred to a "capacitors." To get an idea of the magnitude of the unit Farad, find how large a parallel plate capacitor must be in order to have a capacitance of one Farad. Take the distance between the plates to be 0.1 mm. Capacitors in Electrical Circuits Gaziantep University Faculty of Engineering Department of Engineering Physics 2 The circuit diagram of a capacitor You can "charge" a capacitor by connecting the capacitor to a battery (power supply). (Remember that in the electrostatic situation the wires (conductors) are equipotentials.) Combinations of Capacitors - this is necessary because capacitors with only certain values are available.
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Chapter_5 - General Physics II Capacitors and Dielectrics...

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