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Unformatted text preview: RC Circuits RC Circuits circuits in which the currents vary in time rate of charging a cap depends on C and R of circuit differential equations Discharging a Capacitor Discharging a Capacitor ( sign because q decreases for I > 0 That is, current in circuit equals the decrease of charge on the capacitor) C R qq I Given: R, C, q o (initial charge) Find: q(t) and I(t) when switch is closed dt dq I = 2) 1) = IR C q (Kirchhoff’s Loop Rule) C R qq I RC q dt dq = where: q = q(t) q(0) = q o This is a differential equation for the function q(t), subject to the initial condition q(0) = q 0 . We are looking for a function which is proportional to its own first derivative (since dq/dt ~ q). Combine 1) and 2) to get: RC is called the “time constant ” or “characteristic time” of the circuit. Units: 1 x 1 F = 1 second (show this!) Ω Write τ (“tau”) = RC, then:  = τ t o e q t q ) ( (discharging) RC t ο e q q(t) = Solution: Discharging Discharging q q...
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This note was uploaded on 05/02/2010 for the course PHYSICS 1E03 taught by Professor Jopko during the Spring '08 term at McMaster University.
 Spring '08
 jopko
 Physics, Charge, RC Circuits

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