lecture16 - RC Circuits RC Circuits- circuits in which the...

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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 q-q 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 q-q 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.

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lecture16 - RC Circuits RC Circuits- circuits in which the...

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