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Unformatted text preview: Lecture 7 We saw in an earlier lecture that resistors can be combined in series or in parallel. Capacitors and inductors can also be combined in series or in parallel. Capacitors in Series: .l1--+I~ C1 C2 C3 + Ceq 1 1 1 1 Ceq = C1 + C2 + C3 For k capacitors in series, k C~ = L l/C i q i=l Capacitors in parallel: + Ceq-'------ C3 '-------'---- Ceq = C1 + C2 + C3 For k capacitors in parallel, Ceq = Lr=l C i Inductors behave just like resistors whether they are being combined in series or parallel. In other words, Inductors in series behave as: k Leq = LL i i=l And inductors in parallel as: K L~ = L IJL i q i=l We will move into another topic. So far, we have analyzed circuits that have voltage sources, current sources and resistors only. Sometimes, we have all passive elements (resistors, capacitors, and inductors) in one circuit. We have RL, RC, and RLC circuits. RL and RC circuits are first-order circuits. RL circuits contain power sources, resistors and inductors only, while RC circuits are composed of power sources, resistors and capacitors only. They are so called because their behavior can be modeled with first order differential equations. RLC circuits are second-order circuits and will not be studied in this class. They contain power sources, resistors, capacitors, and inductors only. Before introducing RL, and RC circuits, the iPod analogy may serve a good purpose. Assume that your iPod runs dry on electric charge. Then you connect it to a computer to be charged. After it is disconnected, the iPod charge gradually reduces with time. The gradual decay of charge describes the natural response of the iPod. The iPod has passive elements that use up the charge or energy from the energy storing elements. This is the cause charge or energy from the energy storing elements....
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- Spring '07