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Problem 6: For the circuit shown below, find the phasor current I, the real power, reactive power and apparent power delivered by the source. Find the power factor and draw a power triangle labelling all branches. 1000 v2/0° 100 2 10 μF w = 377

Problem 6: For the circuit shown below, find the phasor current I, the real power, reactive power and apparent power delivered by the source. Find the power factor and draw a power triangle labelling all branches. 1000 v2/0° 100 2 10 μF w = 377

Power System Analysis and Design (MindTap Course List)
Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter6: Power Flows
Section: Chapter Questions
Problem 6.61P
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**Problem 6:** For the circuit shown below, find the phasor current \( I \), the real power, reactive power, and apparent power delivered by the source. Find the power factor and draw a power triangle labeling all branches. **Diagram Description:** - The circuit consists of an AC voltage source with a magnitude of \( 1000 \sqrt{2} \angle 0^\circ \). - A resistor of \( 100 \, \Omega \) is connected in series with the source. - A capacitor with a capacitance of \( 10 \, \mu F \) is also in series. - The angular frequency of the source is \( \omega = 377 \). ### Analysis Steps: 1. **Calculate Phasor Current \( I \):** - Use impedance calculations to find the total impedance of the circuit. - Apply Ohm’s Law to find the current \( I \). 2. **Determine Power Values:** - **Real Power (P):** Calculated as \( P = V \times I \times \cos(\phi) \). - **Reactive Power (Q):** Calculated as \( Q = V \times I \times \sin(\phi) \). - **Apparent Power (S):** Calculated as \( S = V \times I \). 3. **Calculate Power Factor:** - Power Factor \( = \cos(\phi) \), where \( \phi \) is the phase angle between voltage and current. 4. **Draw Power Triangle:** - Represent Real Power, Reactive Power, and Apparent Power on the triangle's horizontal and vertical sides respectively. - Label all sides clearly to illustrate the power relations. This educational problem guides through the practical application of AC circuit analysis involving phasor concepts and power calculations.
Transcribed Image Text:**Problem 6:** For the circuit shown below, find the phasor current \( I \), the real power, reactive power, and apparent power delivered by the source. Find the power factor and draw a power triangle labeling all branches. **Diagram Description:** - The circuit consists of an AC voltage source with a magnitude of \( 1000 \sqrt{2} \angle 0^\circ \). - A resistor of \( 100 \, \Omega \) is connected in series with the source. - A capacitor with a capacitance of \( 10 \, \mu F \) is also in series. - The angular frequency of the source is \( \omega = 377 \). ### Analysis Steps: 1. **Calculate Phasor Current \( I \):** - Use impedance calculations to find the total impedance of the circuit. - Apply Ohm’s Law to find the current \( I \). 2. **Determine Power Values:** - **Real Power (P):** Calculated as \( P = V \times I \times \cos(\phi) \). - **Reactive Power (Q):** Calculated as \( Q = V \times I \times \sin(\phi) \). - **Apparent Power (S):** Calculated as \( S = V \times I \). 3. **Calculate Power Factor:** - Power Factor \( = \cos(\phi) \), where \( \phi \) is the phase angle between voltage and current. 4. **Draw Power Triangle:** - Represent Real Power, Reactive Power, and Apparent Power on the triangle's horizontal and vertical sides respectively. - Label all sides clearly to illustrate the power relations. This educational problem guides through the practical application of AC circuit analysis involving phasor concepts and power calculations.
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