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4. For the circuit shown in Figure 7.4, determine apparent power S, real power P, reactive power Q and power factor PF. Also, draw the power triangle. The source is 120 volts. -j 60 40 Figure 7.4 j 100 E

4. For the circuit shown in Figure 7.4, determine apparent power S, real power P, reactive power Q and power factor PF. Also, draw the power triangle. The source is 120 volts. -j 60 40 Figure 7.4 j 100 E

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
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For the circuit shown in Figure 7.4, determine apparent power S, real power P, reactive power Q
and power factor PF. Also, draw the power triangle. The source is 120 volts.

**Problem Description:** **4. For the circuit shown in Figure 7.4, determine apparent power \( S \), real power \( P \), reactive power \( Q \) and power factor \( PF \). Also, draw the power triangle. The source is 120 volts.** **Figure 7.4:** The diagram represents an AC circuit composed of a voltage source \( E \) which is 120 volts. The circuit components include: - A series impedance \( -j60 \) ohms (inductive reactance) between points \( a \) and \( b \). - A series resistor \( 40 \) ohms between points \( b \) and \( c \). - A parallel impedance \( j100 \) ohms (capacitive reactance) connected between point \( c \) and the ground. **Detailed Analysis:** 1. **Determine Impedance:** - Calculate the total impedance of the circuit - Combine the series and parallel impendances appropriately 2. **Calculate Apparent Power \( S \):** - Use the formula \( S = V \cdot I^* \) - Convert voltage and impedance to phasor forms as needed 3. **Determine Real Power \( P \):** - Use the formula \( P = V \cdot I \cdot \cos(\theta) \) - Determine phase angle \( \theta \) 4. **Determine Reactive Power \( Q \):** - Use the formula \( Q = V \cdot I \cdot \sin(\theta) \) 5. **Calculate Power Factor \( PF \):** - Use the formula \( PF = \cos(\theta) \) 6. **Draw the Power Triangle:** - Apply calculations to illustrate the relationship between \( P \), \( Q \), and \( S \) on a right-angle triangle. **Solution:** 1. **Impedance Calculation:** Combine the series and parallel impedances correctly to find the total impedance \(Z_{total}\): - Series impedance: \(Z_{series} = 40 + (-j60)\) - Summing this with the parallel impedance: Total \( Z = (40 - j60) \parallel j100 \) 2. **Circuit Current Calculation:** Calculate the current, \( I \), using Ohm's Law: \( I = \frac{
Transcribed Image Text:**Problem Description:** **4. For the circuit shown in Figure 7.4, determine apparent power \( S \), real power \( P \), reactive power \( Q \) and power factor \( PF \). Also, draw the power triangle. The source is 120 volts.** **Figure 7.4:** The diagram represents an AC circuit composed of a voltage source \( E \) which is 120 volts. The circuit components include: - A series impedance \( -j60 \) ohms (inductive reactance) between points \( a \) and \( b \). - A series resistor \( 40 \) ohms between points \( b \) and \( c \). - A parallel impedance \( j100 \) ohms (capacitive reactance) connected between point \( c \) and the ground. **Detailed Analysis:** 1. **Determine Impedance:** - Calculate the total impedance of the circuit - Combine the series and parallel impendances appropriately 2. **Calculate Apparent Power \( S \):** - Use the formula \( S = V \cdot I^* \) - Convert voltage and impedance to phasor forms as needed 3. **Determine Real Power \( P \):** - Use the formula \( P = V \cdot I \cdot \cos(\theta) \) - Determine phase angle \( \theta \) 4. **Determine Reactive Power \( Q \):** - Use the formula \( Q = V \cdot I \cdot \sin(\theta) \) 5. **Calculate Power Factor \( PF \):** - Use the formula \( PF = \cos(\theta) \) 6. **Draw the Power Triangle:** - Apply calculations to illustrate the relationship between \( P \), \( Q \), and \( S \) on a right-angle triangle. **Solution:** 1. **Impedance Calculation:** Combine the series and parallel impedances correctly to find the total impedance \(Z_{total}\): - Series impedance: \(Z_{series} = 40 + (-j60)\) - Summing this with the parallel impedance: Total \( Z = (40 - j60) \parallel j100 \) 2. **Circuit Current Calculation:** Calculate the current, \( I \), using Ohm's Law: \( I = \frac{
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