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dv(t) The capacitor in the circuit below is initially uncharged and the switch SW is closed at time t=0. We derived the governing equation in class using KCL (iR-ic) to be V, - v(t) = RC Derive the same equation using KVL. dt V(t) Vs SW ww R .

dv(t) The capacitor in the circuit below is initially uncharged and the switch SW is closed at time t=0. We derived the governing equation in class using KCL (iR-ic) to be V, - v(t) = RC Derive the same equation using KVL. dt V(t) Vs SW ww R .

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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The capacitor in the circuit below is initially uncharged, and the switch SW is closed at time t = 0. We derived the governing equation in class using KCL (iₙ = i_c) to be \( V_s - v(t) = RC \frac{dv(t)}{dt} \). Derive the same equation using KVL. **Diagram Explanation:** - The circuit diagram includes a voltage source (Vs), a switch (SW), a resistor (R), and a capacitor (C). - The current (i) flows through the resistor. - The voltage across the capacitor is labeled \( v(t) \). - The circuit is arranged in a series configuration, starting from the voltage source and passing through the switch and resistor before reaching the capacitor. In the given task, you are required to derive the equation using Kirchhoff's Voltage Law (KVL).
Transcribed Image Text:The capacitor in the circuit below is initially uncharged, and the switch SW is closed at time t = 0. We derived the governing equation in class using KCL (iₙ = i_c) to be \( V_s - v(t) = RC \frac{dv(t)}{dt} \). Derive the same equation using KVL. **Diagram Explanation:** - The circuit diagram includes a voltage source (Vs), a switch (SW), a resistor (R), and a capacitor (C). - The current (i) flows through the resistor. - The voltage across the capacitor is labeled \( v(t) \). - The circuit is arranged in a series configuration, starting from the voltage source and passing through the switch and resistor before reaching the capacitor. In the given task, you are required to derive the equation using Kirchhoff's Voltage Law (KVL).
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