Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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Question
**Determine the following for the network below.** A schematic of an electrical network is shown. It includes a voltage source \( E = 50 \, \text{V} \angle 0^\circ \) with a frequency \( f = 60 \, \text{Hz} \). The circuit contains three components in series: - A resistor \( R \) with a resistance of \( 3 \, \Omega \) - A capacitor \( X_C \) with a reactance of \( 5 \, \Omega \) - An inductor \( X_L \) with a reactance of \( 9 \, \Omega \) **Find the average power delivered to each element.** 1. \( P_R = \) [Input Box] units 2. \( P_C = \) [Input Box] units 3. \( P_L = \) [Input Box] units Please calculate the power delivered to each component using appropriate formulas for resistive and reactive elements in AC circuits.
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Transcribed Image Text:**Determine the following for the network below.** A schematic of an electrical network is shown. It includes a voltage source \( E = 50 \, \text{V} \angle 0^\circ \) with a frequency \( f = 60 \, \text{Hz} \). The circuit contains three components in series: - A resistor \( R \) with a resistance of \( 3 \, \Omega \) - A capacitor \( X_C \) with a reactance of \( 5 \, \Omega \) - An inductor \( X_L \) with a reactance of \( 9 \, \Omega \) **Find the average power delivered to each element.** 1. \( P_R = \) [Input Box] units 2. \( P_C = \) [Input Box] units 3. \( P_L = \) [Input Box] units Please calculate the power delivered to each component using appropriate formulas for resistive and reactive elements in AC circuits.
**Reactive Power Calculation** 1. **Find the reactive power for each element.** - \( Q_R = \) [______] units - \( Q_C = \) [______] units - \( Q_L = \) [______] units 2. **Find the total complex power in rectangular and polar form.** - \( S_T = \) [______] units [______] + j [______] units - \( S_T = \) [______] ∠ [______]° units 3. **Find the total apparent power.** - \( |S_T| = \) [______] units [______] 4. **Using only power quantities, determine the power factor.** - pf = [______] (lagging or leading) [______] **Note:** On your handwritten work, sketch the power triangle to visualize the relationships between the real, reactive, and apparent power.
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Transcribed Image Text:**Reactive Power Calculation** 1. **Find the reactive power for each element.** - \( Q_R = \) [______] units - \( Q_C = \) [______] units - \( Q_L = \) [______] units 2. **Find the total complex power in rectangular and polar form.** - \( S_T = \) [______] units [______] + j [______] units - \( S_T = \) [______] ∠ [______]° units 3. **Find the total apparent power.** - \( |S_T| = \) [______] units [______] 4. **Using only power quantities, determine the power factor.** - pf = [______] (lagging or leading) [______] **Note:** On your handwritten work, sketch the power triangle to visualize the relationships between the real, reactive, and apparent power.
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Step 1: Determine the Unknown variables given in the question:
VIEW
Step 2: Find total impedance of the circuit:
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Step 3: Find current through the circuit:
VIEW
Step 4: Find average power delivered to resistance and capacitance:
VIEW
Step 5: Find average power delivered to inductance:
VIEW
Step 6: Find reactive power delivered to resistor and capacitor:
VIEW
Step 7: Find reactive power delivered to inductor:
VIEW
Step 8: Find total complex power and apparent power:
VIEW
Step 9: Find power factor of the circuit:
VIEW
Solution
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