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Please sketch and label the step input response of Vc(t). Thank you so much!

Please sketch and label the step input response of Vc(t). Thank you so much!

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Please sketch and label the step input response of Vc(t). Thank you so much!

(i) Referring to the R-C circuit shown in Figure 2.0a, assume the switch has been in position "x" long enough so that the capacitor is fully discharged. At time t = 0, the switch is abruptly moved to position “y” connecting the circuit to the voltage source, thereby creating a step-input voltage of Vp. It stays in this position long enough for the capacitor to be fully charged and beyond. Recall, since the voltage across the capacitor does not change instantaneously, then Vc(t) becomes a more convenient variable to characterize the transient response in the "charging" phase than Ic(t). For the above stated conditions, sketch & label the step-input response of Vc(t) and prove that this charging transient response can be expressed as: Vc(t) = Vp(1 e) where T = RC
Transcribed Image Text:(i) Referring to the R-C circuit shown in Figure 2.0a, assume the switch has been in position "x" long enough so that the capacitor is fully discharged. At time t = 0, the switch is abruptly moved to position “y” connecting the circuit to the voltage source, thereby creating a step-input voltage of Vp. It stays in this position long enough for the capacitor to be fully charged and beyond. Recall, since the voltage across the capacitor does not change instantaneously, then Vc(t) becomes a more convenient variable to characterize the transient response in the "charging" phase than Ic(t). For the above stated conditions, sketch & label the step-input response of Vc(t) and prove that this charging transient response can be expressed as: Vc(t) = Vp(1 e) where T = RC
E = Vp - t = 0 €4 Ic(t) C + SWITCH R X Figure 2.0a: R-C circuit with step voltage source + Vc(t)
Transcribed Image Text:E = Vp - t = 0 €4 Ic(t) C + SWITCH R X Figure 2.0a: R-C circuit with step voltage source + Vc(t)
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