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Electric Circuits, 9th Edition P26

Electric Circuits, 9th Edition P26. Designed for use in a one or two-semester Introductory Circuit Analysis or Circuit Theory Course taught in Electrical or Computer Engineering Departments. Electric Circuits 9/e is the most widely used introductory circuits textbook of the past 25 years. As this book has evolved over the years to meet the changing learning styles of students, importantly, the underlying teaching approaches and philosophies remain unchanged. | 226 Response of First-Order RL and RC Circuits constant after the switch has been closed the current will have reached approximately 63 of its final value or z r Vs Vs - e l 0.6321 . R R 7-37 R If the current were to continue to increase at its initial rate it would reach its final value at I rt that is because di _ V5 -l . dt R t Ie Vs . Te 7-38 the initial rate at which z i increases is 7-39 If the current were to continue to increase at this rate the expression for z would be 7.40 from which at t r V L _ L R R 7.41 Figure 7.17 The step response of the RL circuit shown in Fig. 7.16 when 0. 0 t 2r 3r 4t 5t Figure 7.18 Inductor voltage versus time. Equations 7.36 and 7.40 are plotted in Fig. 7.17. The values given by Eqs. 7.37 and 7.41 are also shown in this figure. The voltage across an inductor is Ldi dt so from Eq. 7.35 for t 0 V - 7.42 The voltage across the inductor is zero before the switch is closed. Equation 7.42 indicates that the inductor voltage jumps to Vs - 1 R at the instant the switch is closed and then decays exponentially to zero. Does the value of v at t 0 make sense Because the initial current is 7 and the inductor prevents an instantaneous change in current the current is in the instant after the switch has been closed. The voltage drop across the resistor is I0R and the voltage impressed across the inductor is the source voltage minus the voltage drop that is Vx I R. When the initial inductor current is zero Eq. 7.42 simplifies to v Vs e WL . TA3 If the initial current is zero the voltage across the inductor jumps to Vs. We also expect the inductor voltage to approach zero as t increases because the current in the circuit is approaching the constant value of Vs R. Figure 7.18 shows the plot of Eq. 7.43 and the relationship between the time constant and the initial rate at which the inductor voltage is decreasing. 7.3 The Step Response of RL and RC Circuits 227 If there is an initial current in the inductor Eq. 7.35 gives the solution for it. .