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lesson30

lesson30 - Lesson 30 RL and RC Circuits(Exponential and...

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Lesson 30 – RL and RC Circuits (Exponential and Sinusoidal Transient Responses) (Section 7-4) (CLO 7-2) This lesson is somewhat mathematically challenging since we will be differentiating exponentials and sinusoids. However, the concepts are easy to understand. Start with a first-order circuit driven by an exponential. This is mathematically easier to solve than the sinusoidal driven circuit. The basic equation is as derived earlier The u ( t ) implies that the driving signal v T ( t ) has a finite start time arbitrarily selected as t = 0. This implies that there is an initial condition, v (0) = V 0 , that will have to satisfy the basic equation. As with the step response, we find the solution in two parts: natural response and forced response. The natural response of a stable first-order circuit is of the form The natural response of a first-order circuit always has this form because it is a general solution of the homogeneous equation with the input set to zero. The form of the natural response depends on the physical characteristics of the circuit and is independent of the input. Be sure the students understand this. The forced response v F ( t ), depends on both the circuit and the nature of the forcing function (the input). The forced response is a particular solution of the equation 0 ) ( ) ( ) ( T F F T = + t t v t v dt t dv C R

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