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Consider the circuit below. In this circuit Vs = 10 Volts, R = 10000, C = 1μµF, L = : 1µH. Identify the correct pair of voltage (across capacitor) and current (either inductor or capacitor) + VR(t) AAA

Consider the circuit below. In this circuit Vs = 10 Volts, R = 10000, C = 1μµF, L = : 1µH. Identify the correct pair of voltage (across capacitor) and current (either inductor or capacitor) + VR(t) AAA

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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**Transcription for Educational Website** --- **Problem Statement:** Consider the circuit below. In this circuit \( V_s = 10 \text{ Volts}, \ R = 1000 \Omega, \ C = 1 \mu F, \ L = 1 \mu H. \) Identify the correct pair of voltage (across capacitor) and current (either inductor or capacitor). --- **Circuit Diagram:** The diagram displays a simple series RLC circuit with the following components: - A voltage source, \( V_s \). - A resistor \( R \) with voltage across it denoted as \( V_R(t) \). - A capacitor \( C \) with voltage across it denoted as \( V_C(t) \). - An inductor \( L \) with current through it denoted as \( I_L(t) \) and voltage across it \( V_L(t) \). The switch in the circuit is closed at \( t = 0 \). --- **Answer Options:** - **a.** \[ V_C(t) = 10 \sin(2\pi \times 10^6 t), \quad I_C(t) = 10 \sin(2\pi \times 10^6 t) \] - **b.** \[ V_C(t) = 10 \sin(10^6 t), \quad I_L(t) = 10 \cos(10^6 t) \] - **c.** \[ V_C(t) = 10 \cos(10^6 t), \quad I_L(t) = 10 \sin(10^6 t) \] - **d.** \[ V_C(t) = 10 \cos(2\pi \times 10^6 t), \quad I_L(t) = -10 \sin(2\pi \times 10^6 t) \] --- **Instructions:** Select the correct pair of mathematical functions that represent the voltage across the capacitor and the current through either the inductor or the capacitor in this circuit configuration.
Transcribed Image Text:**Transcription for Educational Website** --- **Problem Statement:** Consider the circuit below. In this circuit \( V_s = 10 \text{ Volts}, \ R = 1000 \Omega, \ C = 1 \mu F, \ L = 1 \mu H. \) Identify the correct pair of voltage (across capacitor) and current (either inductor or capacitor). --- **Circuit Diagram:** The diagram displays a simple series RLC circuit with the following components: - A voltage source, \( V_s \). - A resistor \( R \) with voltage across it denoted as \( V_R(t) \). - A capacitor \( C \) with voltage across it denoted as \( V_C(t) \). - An inductor \( L \) with current through it denoted as \( I_L(t) \) and voltage across it \( V_L(t) \). The switch in the circuit is closed at \( t = 0 \). --- **Answer Options:** - **a.** \[ V_C(t) = 10 \sin(2\pi \times 10^6 t), \quad I_C(t) = 10 \sin(2\pi \times 10^6 t) \] - **b.** \[ V_C(t) = 10 \sin(10^6 t), \quad I_L(t) = 10 \cos(10^6 t) \] - **c.** \[ V_C(t) = 10 \cos(10^6 t), \quad I_L(t) = 10 \sin(10^6 t) \] - **d.** \[ V_C(t) = 10 \cos(2\pi \times 10^6 t), \quad I_L(t) = -10 \sin(2\pi \times 10^6 t) \] --- **Instructions:** Select the correct pair of mathematical functions that represent the voltage across the capacitor and the current through either the inductor or the capacitor in this circuit configuration.
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