The voltage source (V1) in the circuit is given by: v(t) = 15 * cos(5x10ft) V If L1 = 1 mH, R1 = 10 02 Determine > V1 a) the complex power supplied by the source b) the power factor of the source c) the complex power for each passive element L1 R1
The voltage source (V1) in the circuit is given by: v(t) = 15 * cos(5x10ft) V If L1 = 1 mH, R1 = 10 02 Determine > V1 a) the complex power supplied by the source b) the power factor of the source c) the complex power for each passive element L1 R1
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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![**Educational Transcription**
### Circuit Analysis Problem
#### Circuit Description:
The circuit consists of a voltage source (V1), an inductor (L1), and a resistor (R1) connected in series.
#### Voltage Source:
The voltage source \( V1 \) in the circuit is defined by the equation:
\[ v(t) = 15 \times \cos(5 \times 10^4 t) \, \text{V} \]
#### Circuit Components:
- Inductance \( L1 = 1 \, \text{mH} \)
- Resistance \( R1 = 10 \, \Omega \)
#### Tasks:
Determine the following electrical properties of the circuit:
a) **The complex power supplied by the source:**
- This involves calculating the apparent power (\( S \)), which combines both the real power (\( P \)) and reactive power (\( Q \)).
b) **The power factor of the source:**
- The power factor describes how effectively the electric power is being converted into useful work. It is the cosine of the phase angle between the voltage and current waveforms.
c) **The complex power for each passive element:**
- Calculate the complex power for both \( L1 \) and \( R1 \). The inductor will mainly have reactive power, while the resistor will have real power.
#### Diagram Explanation:
The diagram illustrates a simple series circuit:
- **Voltage Source (V1):** Located on the left, providing the circuit's AC voltage.
- **Inductor (L1):** Symbolized by a coil, indicating its reactive nature.
- **Resistor (R1):** Shown as a zigzag line, indicating resistance.
This configuration is a typical R-L circuit, used to analyze AC circuit behavior, especially in determining impedance, power factors, and power distribution across circuit components.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe082a62-4024-470b-9494-09a6e9a82c01%2Ff731c90a-7159-449d-951e-6cb9acdd8f95%2Fotep5h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Transcription**
### Circuit Analysis Problem
#### Circuit Description:
The circuit consists of a voltage source (V1), an inductor (L1), and a resistor (R1) connected in series.
#### Voltage Source:
The voltage source \( V1 \) in the circuit is defined by the equation:
\[ v(t) = 15 \times \cos(5 \times 10^4 t) \, \text{V} \]
#### Circuit Components:
- Inductance \( L1 = 1 \, \text{mH} \)
- Resistance \( R1 = 10 \, \Omega \)
#### Tasks:
Determine the following electrical properties of the circuit:
a) **The complex power supplied by the source:**
- This involves calculating the apparent power (\( S \)), which combines both the real power (\( P \)) and reactive power (\( Q \)).
b) **The power factor of the source:**
- The power factor describes how effectively the electric power is being converted into useful work. It is the cosine of the phase angle between the voltage and current waveforms.
c) **The complex power for each passive element:**
- Calculate the complex power for both \( L1 \) and \( R1 \). The inductor will mainly have reactive power, while the resistor will have real power.
#### Diagram Explanation:
The diagram illustrates a simple series circuit:
- **Voltage Source (V1):** Located on the left, providing the circuit's AC voltage.
- **Inductor (L1):** Symbolized by a coil, indicating its reactive nature.
- **Resistor (R1):** Shown as a zigzag line, indicating resistance.
This configuration is a typical R-L circuit, used to analyze AC circuit behavior, especially in determining impedance, power factors, and power distribution across circuit components.
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