**Power Factor Corrections**Given \( v_s(t) = 110 \, \sqrt{2} \cos(1000t) \, \text{V} \) is the time domain voltage equation on the schematic in Fig. 2. Find the capacitance of \( C_X \) such that the power factor is equal to 1.---### Diagram Explanation**Figure 2: Circuit Problem 2**This is an electrical circuit diagram. The components and their values are:1. **Voltage Source (\( v_s(t) \))**: Alternating current source, defined by the equation \( v_s(t) = 110 \, \sqrt{2} \cos(1000t) \, \text{V} \).2. **Resistor (\( R_1 \))**: 15 ohms (\( \Omega \)).3. **Capacitor (\( C_X \))**: Unknown capacitance. It is the component that needs to be calculated for the power factor correction.4. **Inductor (\( L_1 \))**: 50 millihenries (mH).5. **Resistor**: 5 ohms (\( \Omega \)), connected in series with another capacitor.6. **Capacitor (\( C_2 \))**: Labeled with current \( I_{C2} \).7. **Inductor (\( L_2 \))**: 10 ohms (\( \Omega \)), labeled with current \( I_{L2} \).The circuit's goal is to adjust the unknown capacitor \( C_X \) such that the overall power factor of the circuit is corrected to 1, indicating a purely resistive circuit.

Given Vs(t)=110 2cos(1000t)V calculate Cx in the below circuit

Power Factor corrections Given us(t) = 110 2 cos(1000t) V is the time domain voltage equation on the schematic in Fig. 2 Find the capacitance of Cx such as the power factor is equal to 1. Us(t) + IT R₁ 1592 Cx H} ?? L₁ oooo 50mH Figure 2: Circuit Problem 2 Ic₂ 592=C₂ 112 100 L₂

Power Factor corrections Given us(t) = 110 2 cos(1000t) V is the time domain voltage equation on the schematic in Fig. 2 Find the capacitance of Cx such as the power factor is equal to 1. Us(t) + IT R₁ 1592 Cx H} ?? L₁ oooo 50mH Figure 2: Circuit Problem 2 Ic₂ 592=C₂ 112 100 L₂

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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Question

**Power Factor Corrections**

Given \( v_s(t) = 110 \, \sqrt{2} \cos(1000t) \, \text{V} \) is the time domain voltage equation on the schematic in Fig. 2. Find the capacitance of \( C_X \) such that the power factor is equal to 1.

---

### Diagram Explanation

**Figure 2: Circuit Problem 2**

This is an electrical circuit diagram. The components and their values are:

1. **Voltage Source (\( v_s(t) \))**: Alternating current source, defined by the equation \( v_s(t) = 110 \, \sqrt{2} \cos(1000t) \, \text{V} \).

2. **Resistor (\( R_1 \))**: 15 ohms (\( \Omega \)).

3. **Capacitor (\( C_X \))**: Unknown capacitance. It is the component that needs to be calculated for the power factor correction.

4. **Inductor (\( L_1 \))**: 50 millihenries (mH).

5. **Resistor**: 5 ohms (\( \Omega \)), connected in series with another capacitor.

6. **Capacitor (\( C_2 \))**: Labeled with current \( I_{C2} \).

7. **Inductor (\( L_2 \))**: 10 ohms (\( \Omega \)), labeled with current \( I_{L2} \).

The circuit's goal is to adjust the unknown capacitor \( C_X \) such that the overall power factor of the circuit is corrected to 1, indicating a purely resistive circuit.

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