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Pre-Lab Problem Consider the electrical RC circuit shown in the illus- tration. The resistance R 10 kn, and the capacitance C = 0.1 µF. Part I Vs(t) ( R www] C a) Suppose that at t = 0, the voltage on the capac- itor ve(0) = 0, and that the input voltage source is a step v. (t) = Vous(t). First, assume that the output is voltage across the capacitor. Derive the differential equation relating ve(t) to the input volt- age v₂(t). b) Solve the differential equation in part a). That is, derive an expression for ve(t). c) From the results of part b), find the voltage across the resistor u, (t). Hint: It is not necessary to de- rive or solve any additional differential equations. Consider the loop equation.

Pre-Lab Problem Consider the electrical RC circuit shown in the illus- tration. The resistance R 10 kn, and the capacitance C = 0.1 µF. Part I Vs(t) ( R www] C a) Suppose that at t = 0, the voltage on the capac- itor ve(0) = 0, and that the input voltage source is a step v. (t) = Vous(t). First, assume that the output is voltage across the capacitor. Derive the differential equation relating ve(t) to the input volt- age v₂(t). b) Solve the differential equation in part a). That is, derive an expression for ve(t). c) From the results of part b), find the voltage across the resistor u, (t). Hint: It is not necessary to de- rive or solve any additional differential equations. Consider the loop equation.

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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Pre-Lab Problem Consider the electrical RC circuit shown in the illus- tration. The resistance R 10 kn, and the capacitance C = 0.1 µF. Part I Vg(t) ( R www] C a) Suppose that at t = 0, the voltage on the capac- itor ve(0) = 0, and that the input voltage source is a step v. (t) = Vous(t). First, assume that the output is voltage across the capacitor. Derive the differential equation relating ve(t) to the input volt- age v₂(t). b) Solve the differential equation in part a). That is, derive an expression for ve(t). c) From the results of part b), find the voltage across the resistor u, (t). Hint: It is not necessary to de- rive or solve any additional differential equations. Consider the loop equation.
Transcribed Image Text:Pre-Lab Problem Consider the electrical RC circuit shown in the illus- tration. The resistance R 10 kn, and the capacitance C = 0.1 µF. Part I Vg(t) ( R www] C a) Suppose that at t = 0, the voltage on the capac- itor ve(0) = 0, and that the input voltage source is a step v. (t) = Vous(t). First, assume that the output is voltage across the capacitor. Derive the differential equation relating ve(t) to the input volt- age v₂(t). b) Solve the differential equation in part a). That is, derive an expression for ve(t). c) From the results of part b), find the voltage across the resistor u, (t). Hint: It is not necessary to de- rive or solve any additional differential equations. Consider the loop equation.
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