lesson29

# lesson29 - Lesson 29 RL and RC Circuits(Step...

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v T (t) R T C + _ v C (t) i (t) v C (0)=V O Lesson 29 – RL and RC Circuits (Step Response) (Sections 7-2 and 7-3) (CLO 7-1) This lesson starts out challenging but fortunately becomes easy for the students to use once the derivations are done and they can apply solutions to a template. That this analysis becomes relatively “plug-and-chug” is a mixed blessing. It makes students capable of designing simple timing circuits but often disguises understanding of what is really occurring. At least part of the secret to increasing understanding is to have students find parameters other than v C ( t ) or i L ( t ) . Start the lesson by continuing from the last lesson. Quickly repeat the derivation of the first-order differential equation of an RC circuit. Here it is again: ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( t v dt t dv RC t v t v t Ri t v t v t v t v C C T C T C R T + = + = + = Substitute for i ( t ) =Cdv C ( t ) /dt Remind the students that unlike dc circuits with only sources and resistors RL and RC circuits can store energy. This energy, we saw last time, gives rise to a response even after the power is turned off. Therefore, while this feature complicates things it makes wonderful, practical circuits possible. Going back to our equation we now need to solve our circuit for cases where there is an input, v T (t) . To solve RL and RC circuits under these conditions one needs to know three things:

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lesson29 - Lesson 29 RL and RC Circuits(Step...

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