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Lecture 10: RL & RC Circuits Nilsson & Riedel 7.1-7.6 ENG17 (Sec. 2): Circuits I Spring 2014 1 May 1, 2014

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Recap – Inductors / Capacitors 2

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Overview Natural Response –RL Circuits –RC Circuits Step Response –RL Circuits –RC Circuits General Solution Sequential Switching Unbounded Response 3

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Natural Response 4 Currents and voltages that arise from an inductor or capacitor immediately after being disconnected from a DC (direct current) source.

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Current in RL Circuit 5 After Open Switch

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Time Constant 6

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RL Circuit Example 7

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Voltage in RC Circuit 8 After Switching

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RC Circuit Example 9

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Overview Natural Response –RL Circuits –RC Circuits Step Response –RL Circuits –RC Circuits General Solution Sequential Switching Unbounded Response 10

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Step Response 11 Currents and voltages that arise when energy is being acquired by an inductor or capacitor due to the sudden application of a dc voltage or current source.

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Step Response in RL Circuit 12

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Step Response in RC Circuit 13

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Overview Natural Response –RL Circuits –RC Circuits Step Response –RL Circuits –RC Circuits General Solution Sequential Switching Unbounded Response 14

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Generalized Solution 15

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Overview Natural Response –RL Circuits –RC Circuits Step Response –RL Circuits –RC Circuits General Solution Sequential Switching Unbounded Response 16

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Sequential Switching 17 Defined: whenever switching occurs more than once in a circuit

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Overview Natural Response –RL Circuits –RC Circuits Step Response –RL Circuits –RC Circuits General Solution Sequential Switching Unbounded Response 18

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Unbounded Response Defined: A circuit response that grows, rather than decays, exponentially with time. Possible with dependent sources 19

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Recap Natural Response –RL Circuits –RC Circuits Step Response –RL Circuits –RC Circuits General Solution Sequential Switching Unbounded Response 20

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ADDING INTEGERS 1. POS. + POS. = POS. 2. NEG. + NEG. = NEG. 3. POS. + NEG. OR NEG. + POS. SUBTRACT TAKE SIGN OF BIGGER ABSOLUTE VALUE.

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