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Consider the following RC circuit, what are values of V (+∞) and Vc (0)? Vo t=0 R V C ic

Consider the following RC circuit, what are values of V (+∞) and Vc (0)? Vo t=0 R V C ic

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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Hint: when t<0, the switch is closed, and the switch will be opened at t=0. For t>0, the switch remains open. Let us travel the time axis to analyze this circuit: 8118 Switch is closed Switch is closed Switch is open t=0 t = 0+ t=0 t=48 Switch is open First, at t=-∞, the switch is closed, and the voltage source Vo begins to charge the capacitor C. Next, consider t=0, which is the time step just before t=0. At this moment, the switch is still closed since we have not reached t=0 yet. Besides, the capacitor C is fully charged, and its voltage is stabilized. In this case, the capacitor is equivalent to an open circuit, i.e., ic = 0. Then, consider t=0+, which is the time instant immediately after t=0. At this time, the switch is open. One important feature of capacitors is that the voltage on a capacitor can't be suddenly changed, i.e., the voltage on a capacitor is a continuous value. Thus, Vc (0+) = Vc (0¯). Finally, consider t=+∞. After disconnecting from the voltage source for a long time, the energy stored inside the capacitor is all dissipated. O Ve (0) = Voi V₂ (+∞o) = 0 O Ve (0) = 0; Ve(+∞o) = Vo O Ve (0)=ie C; Vc (+∞0) = 0 O Ve (0) = Voi Ve (+00) = in R
Transcribed Image Text:Hint: when t<0, the switch is closed, and the switch will be opened at t=0. For t>0, the switch remains open. Let us travel the time axis to analyze this circuit: 8118 Switch is closed Switch is closed Switch is open t=0 t = 0+ t=0 t=48 Switch is open First, at t=-∞, the switch is closed, and the voltage source Vo begins to charge the capacitor C. Next, consider t=0, which is the time step just before t=0. At this moment, the switch is still closed since we have not reached t=0 yet. Besides, the capacitor C is fully charged, and its voltage is stabilized. In this case, the capacitor is equivalent to an open circuit, i.e., ic = 0. Then, consider t=0+, which is the time instant immediately after t=0. At this time, the switch is open. One important feature of capacitors is that the voltage on a capacitor can't be suddenly changed, i.e., the voltage on a capacitor is a continuous value. Thus, Vc (0+) = Vc (0¯). Finally, consider t=+∞. After disconnecting from the voltage source for a long time, the energy stored inside the capacitor is all dissipated. O Ve (0) = Voi V₂ (+∞o) = 0 O Ve (0) = 0; Ve(+∞o) = Vo O Ve (0)=ie C; Vc (+∞0) = 0 O Ve (0) = Voi Ve (+00) = in R
For an RC circuit (RC stands for Resistor and Capacitor), the voltage on the capacitor follows this expression: Vc (t) = K₁ + K₂ e , T = R.C · where K₁ = Vc (+00), K₁1 + K₂ = Vc (0). To find V. (t), we need to figure out what values of Ve (+) and Vc (0) are, then, we can solve for K₁ and K₂. Consider the following RC circuit, what are values of V (+∞) and Vc (0)? + t = 0 Switch is closed t=0 Hint: when t<0, the switch is closed, and the switch will be opened at t=0. For t>0, the switch remains open. Let us travel the time axis to analyze this circuit: + Ry – С ic Switch is open t = 0
Transcribed Image Text:For an RC circuit (RC stands for Resistor and Capacitor), the voltage on the capacitor follows this expression: Vc (t) = K₁ + K₂ e , T = R.C · where K₁ = Vc (+00), K₁1 + K₂ = Vc (0). To find V. (t), we need to figure out what values of Ve (+) and Vc (0) are, then, we can solve for K₁ and K₂. Consider the following RC circuit, what are values of V (+∞) and Vc (0)? + t = 0 Switch is closed t=0 Hint: when t<0, the switch is closed, and the switch will be opened at t=0. For t>0, the switch remains open. Let us travel the time axis to analyze this circuit: + Ry – С ic Switch is open t = 0
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