Physics2Ch19-20 - PHY1004W 2010 Electricity and Magnetism...

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Prof Andy Buffler Room 503 RW James andy.buffler@uct.ac.za PHY1004W 2010 Electricity and Magnetism Part 3
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M&I Chapter 19 Capacitors, Resistors and Batteries
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Capacitors in circuits M&I 19.1 Surface charge rearrangements are rapid … nanoseconds! … a steady state is soon reached. … capacitors can be used to cause a slower change of the current in a circuit … Capacitor: or A capacitor is made of a sandwich of two metal foils separated by an insulating material and coiled up into a small package. … no conducting path through the capacitor … charges cannot jump between the plates. insulating material external connections
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A charged capacitor (charge Q on each plate): fringe 0 2 Q A s E R    Radius, R Plate separation s E fringe Plate area A There is a fringe field just outside the charged capacitor plates, where . ..
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M&I 19.2 Charging a capacitor Connect a 6V battery, a light bulb and a capacitor in series . .. At t = 0.1 s after starting, the bulb shines brightly . .. At t = 1 s after starting, the bulb is down to medium brightness . .. At t > 10 s after starting, the bulb is not glowing at all . ..
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Charging a capacitor . .. 2 After some time, there is significant positive and negative charge on the capacitor plates . .. ... the fringe field of the capacitor acts in a direction opposite to the conventional current, thus decreasing the net field and the current decreases. Eventually the current stops when there is enough charge on the capacitor to create large enough fringe field to counteract the field made by the other charges. The initial establishment of surface charges takes a few nanoseconds, while it takes several seconds to reach static equilibrium (zero current).
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Discharging a capacitor Now remove the battery completely . .. t = 0.1 s t = 1 s t > 10 s The light bulb initially burns brightly again and decays in brightness until the current in the circuit is once again zero . .. The fringe field of the capacitor plus the electric field of the charges on the surfaces of the wires drives the current so as to reduce the charge on the capacitor plates . .. and on the wire surfaces . .. the electric field is reduced and so thus the current.
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a. Different plate radius R: fringe,1 2 0 1 0 1 1 22 Q A s Q s E R R R    R 1 R 2 > R 1 Same charge Q distributed on plates after 0.01 s of charging in each case . .. fringe,2 fringe,1 2 0 2 0 2 2 Q A s Q s EE R R R Smaller fringe field means a larger net field, hence current in circuit with larger capacitor has decreased less than smaller capacitor. Applications M&I 19.5
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b. Different plate separation s : Same charge Q distributed on plates after 0.01 s of charging in each case. .. s 1 s 2 < s 1 1 fringe,1 0 2 s QA E R    2 fringe,2 fringe,1 0 2 s EE R  Again, a smaller fringe field means a larger net field, hence current in circuit with larger capacitor has decreased less than smaller capacitor.
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Physics2Ch19-20 - PHY1004W 2010 Electricity and Magnetism...

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