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L14 first - Circuit Elements Resistor(i v characteris;c v R...

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3/12/14 1 Circuit Elements Resistor v R i R v R = R i R i R = v R R P R = i R 2 R (i-­‐v) characteris;c Power P R = v R 2 R Circuit Elements Capacitor (i-­‐v) characteris;c v c = v c ( t o ) + 1 C i c dt t 0 t i c = C dv c dt v c i c P c = v c [ ] C dv c dt P c = i c [ ] v c ( t o ) + 1 C i c dt t 0 t W c = 1 2 C v c 2 Energy stored Power or
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3/12/14 2 Power Inductor (i-­‐v) characteris;c v L = L di L dt i L = i L ( t o ) + 1 L v L dt t 0 t P L = v L [ ] i L ( t o ) + 1 L v L dt t 0 t P L = i L [ ] L di L dt Energy stored W L = 1 2 L i L 2 v L i L First order circuits Circuits contains on dynamic element ( capacitor or inductor) Examples: v s ( t ) R L i s ( t ) R L R C v s ( t ) R C i s ( t ) RL circuit RL circuit RC circuit RC circuit
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3/12/14 3 i s ( t ) R L i L ( t ) v L ( t ) i R ( t ) i s = i L + i R KCL: i s = i L + v R i s = i L + 1 R L di L dt di L dt + R L i L = R L i s The circuit differen;al equa;on in terms of i L a) RL circuit Analysis of first order circuits Check Dimensions! di L dt + R L i L = R L i s R = Volt current L = flux current = volt time current L R = volt time current current volt = time Define: L R = τ Circuit ;me constant! Note : L R = τ = s
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3/12/14 4 v s = v c + v R KVL: v s = v c + i c R v s = v c + R C dv c dt dv c dt + 1 RC v c = 1 RC v s The circuit differen;al equa;on in terms of v c i c ( t ) v c ( t ) i R ( t ) R C v s ( t ) v
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