Ee 442 rc and rl transients 20 the quantitative

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Unformatted text preview: ty similar to the one obtained in the RC circuit. And the solution is nearly identical. EE 442 RC and RL transients – 19 diL dt = IS − iL L/R ￿t ￿ iL ( t ) ￿ dt￿ diL ￿= I S − iL 0 L/R ILi ￿ IL (t ) ￿ ￿ ￿￿ ln [IS − iL ] ￿ = ILi After some re-arrangement: t 0 ￿t t￿ ￿ L/R ￿ ￿ 0 ￿ t iL (t) = IS − (IS − ILi ) exp − L /R ￿ Note the similarity to the capacitor equation. Replace voltages with currents and RC with L/R, and they are identical. EE 442 RC and RL transients – 20 The quantitative result matches the earlier qualitative argument exactly. At t = 0: IL (t = 0) = ILi (= 0) VL (t = 0) = 0 After a long time, (t → ∞ ) IL (t → ∞) = IS VL (t → ∞) = 0 In between, the inductor current changes, in an exponential fashion, from ILi to IS. The voltage jumps to an initial value and then decays exponentially to zero. Since this all happens within a given timespan, these are known as inductor transient effects. EE 442 RC and RL transients – 21 Plots of inductor current and voltage for a circuit with IS = 4 mA, ILi = 0, R = 2.5 kΩ, R = 5 H (L/R = 2 ms). EE 442 RC and RL transients – 22 The RC and RL transient equations are so similar and apply to so many different situations, that is worth memorizing them. More importantly, in any case where a single capacitor or inductor is being switched into or out of a circuit, it is probably easier to make the “circuit fit the analysis”. In other words, use the Thevenin or Norton equivalent equivalent of the circuit attached to capacitor or inductor to make the problem look exactly like the prototypes that we just studied. EE 442 RC and RL transients – 23...
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This document was uploaded on 04/05/2014.

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