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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 (Kirchhoffs 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!) Write (tau) = RC, then:  = t o e q t q ) ( (discharging) RC t e q q(t) = Solution: Discharging Discharging q q...
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This note was uploaded on 01/23/2011 for the course ENG 1D04 taught by Professor Done during the Spring '08 term at McMaster University.
 Spring '08
 DONE

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