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Unformatted text preview: Physics II Electricity and Magnetism Waves and Oscillations Modern Physics 1 What Is a Capacitor? A device that stores charge when a potential difference is applied The ratio of charge stored to potential difference maintained is the capacitance of the object
V + q C= V -q q is the magnitude of the charge on one plate V +q 2 Capacitance
q C= V q = CV q is the magnitude of the equal + and charges on the plates of the capacitor. V is really V, the potential difference between the two plates of the capacitor. 3 Units
q is in Coulombs V is in Volts C is in Farads C depends on the dimensions of the capacitor, not on q or V. 4 Example: A Parallel Plate Capacitor
q A C = = 0 V d Notice that capacitance increases with increased area, and decreases with increased distance between the plates. 5 Capacitors in Parallel V is the same q1 = C1V q2 = C2V Total charge = q = q1 + q2 q (C1 + C2 )V C= = V V C = C1 + C2 6 Capacitors in Series q is the same
q V1 = C1 q V2 = C2 q q V = V1 + V2 = + C1 C2 V 1 1 1 = = + q C C1 C2 7 Capacitors Store Energy U = 1 qV 2 or, since q = CV q U = CV = 2C
1 2 2 2 8 Energy Density U = CV
1 2 2 A C = 0 , and V = Ed , so d A 2 2 1 2 1 U = 2 0 E d = 2 0 AdE d U 2 1 = u = 2 0E Ad 9 Energy Density The energy in a capacitor is stored in the electric field between the plates. Ad is the volume between the plates, so 2 1 u = 2 0E is the energy per volume in the electric field between the plates. This result is true for all electric fields. 10 Concepts to remember Capacitance Capacitors Energy density 11 ...
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