le10 - E E 2315 Lecture 10 Natural and Step Responses of RL...

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315 E E 2315 Lecture 10 atural and Step Responses of RL Natural and Step Responses of RL and RC Circuits
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10/27/2009 1 Conservation of Charge (1/4) • Energy transferred if v 10 v 20 • Total system charge is conserved Conservation of Charge (2/4) Initial stored energy: At equilibrium: Conservation of Charge (3/4) Initial Charge: Final Charge: Since
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10/27/2009 2 Conservation of Charge (4/4) Final stored energy: Energy consumed in R: Conservation of Flux Linkage (1/3) • Energy transferred if i 10 i 20 • Total system flux linkage is conserved. Initial stored energy: At equilibrium: Conservation of Flux Linkage (2/3) Initial flux linkage: Final flux linkage: Since
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10/27/2009 3 Conservation of Flux Linkage (3/3) Final stored energy: Energy consumed in R: Natural RL Response (1/2) • Inductor has initial current, i o . • Switch opens at t = 0 • Inductor current can’t change instantaneousl instantaneously Natural RL Response (2/2) Integrate: KVL: Separate the variables: Exponential of both sides:
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le10 - E E 2315 Lecture 10 Natural and Step Responses of RL...

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