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(1) The system is in steady state. The phasor diagram shows the voltages V₁ and V₁ (but you are not told which one is which). The current source is a sine wave with w = 1 rad/s. (s)-5√√2√ 2.5A (a) Find v₁ (3 s), i.e., v; at time t = 3π 4 (b) What is the value of A? (c) What is the value of capacitor Ca? is A sin(wt + 0) + Vi seconds. 1 H ΖΩ Ca Vb + Va Vi 3π A Ca C = 1/2 F and C = 3/2 F Im 5j I 5 Re

(1) The system is in steady state. The phasor diagram shows the voltages V₁ and V₁ (but you are not told which one is which). The current source is a sine wave with w = 1 rad/s. (s)-5√√2√ 2.5A (a) Find v₁ (3 s), i.e., v; at time t = 3π 4 (b) What is the value of A? (c) What is the value of capacitor Ca? is A sin(wt + 0) + Vi seconds. 1 H ΖΩ Ca Vb + Va Vi 3π A Ca C = 1/2 F and C = 3/2 F Im 5j I 5 Re

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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--- **Educational Content: Steady State System Analysis** **(1)** The system is in steady state. The phasor diagram represents the voltages \( V_a \) and \( V_b \). The identity of the voltages is not specified. The current source produces a sine wave with \(\omega = 1 \, \text{rad/s}\). - **(a)** Determine \( v_i \left( \frac{3\pi}{4} \, \text{s} \right) \), i.e., \( v_i \) at time \( t = \frac{3\pi}{4} \) seconds. \[ v_i \left( \frac{3\pi}{4} \, \text{s} \right) = -5\sqrt{2} \] - **(b)** Identify the value of \( A \). \[ A = 2.5\, \text{A} \] - **(c)** Determine the value of capacitor \( C_a \). \[ C = \frac{1}{2} \, \text{F and} \, C = \frac{3}{2} \, \text{F} \] **Circuit Diagram Explanation:** - The diagram includes an inductor and a capacitor connected in series with a resistor (2 Ω). - The inductor value is 1 H. - The voltage across the components are labeled \( v_a \) and \( v_b \). - The current source is represented as \( i_s = A \cdot \sin(\omega t + \theta) \). **Phasor Diagram Explanation:** - The phasor diagram includes a real and imaginary axis, represented as \( \text{Re} \) and \( \text{Im} \). - A phasor with a magnitude of 5 is shown along the real axis. - Another phasor with a magnitude of \( 5j \) (representing the imaginary component) is indicated on the imaginary axis. ---
Transcribed Image Text:--- **Educational Content: Steady State System Analysis** **(1)** The system is in steady state. The phasor diagram represents the voltages \( V_a \) and \( V_b \). The identity of the voltages is not specified. The current source produces a sine wave with \(\omega = 1 \, \text{rad/s}\). - **(a)** Determine \( v_i \left( \frac{3\pi}{4} \, \text{s} \right) \), i.e., \( v_i \) at time \( t = \frac{3\pi}{4} \) seconds. \[ v_i \left( \frac{3\pi}{4} \, \text{s} \right) = -5\sqrt{2} \] - **(b)** Identify the value of \( A \). \[ A = 2.5\, \text{A} \] - **(c)** Determine the value of capacitor \( C_a \). \[ C = \frac{1}{2} \, \text{F and} \, C = \frac{3}{2} \, \text{F} \] **Circuit Diagram Explanation:** - The diagram includes an inductor and a capacitor connected in series with a resistor (2 Ω). - The inductor value is 1 H. - The voltage across the components are labeled \( v_a \) and \( v_b \). - The current source is represented as \( i_s = A \cdot \sin(\omega t + \theta) \). **Phasor Diagram Explanation:** - The phasor diagram includes a real and imaginary axis, represented as \( \text{Re} \) and \( \text{Im} \). - A phasor with a magnitude of 5 is shown along the real axis. - Another phasor with a magnitude of \( 5j \) (representing the imaginary component) is indicated on the imaginary axis. ---
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