(a)
Find the apparent power delivered to each load in the circuit in Figure 11.45 in the textbook and power factor of the source.
(a)
Answer to Problem 43E
The apparent power delivered to
Explanation of Solution
Given data:
Refer to Figure 11.45 in the textbook for the given circuit.
The impedance of the loads are given as follows:
Formula used:
Write the expression for complex power delivered to the load as follows:
Here,
Write the expression for voltage in terms of current and impedance as follows:
Write the expression for complex power in the rectangular form as follows:
Here,
Write the expression for power factor as follows:
Calculation:
Consider the current through the left-loop as
Apply KVL to the left-loop as follows:
Substitute
Apply KVL to the right-loop as follows:
Substitute
From Equation (6), substitute
Simplify the expression as follows:
Substitute
Modify the expression in Equation (2) for the voltage across the load
Substitute
Modify the expression in Equation (1) for the complex power delivered to the load
Substitute
Find the apparent power delivered to the load
Modify the expression in Equation (2) for the voltage across the load
Substitute
Find the current through the load
Substitute
Modify the expression in Equation (1) for the complex power delivered to the load
Substitute
Find the apparent power delivered to the load
Modify the expression in Equation (2) for the voltage across the load
Substitute
Modify the expression in Equation (1) for the complex power delivered to the load
Substitute
Find the apparent power delivered to the load
Modify the expression in Equation (2) for the voltage across the load
Substitute
Modify the expression in Equation (1) for the complex power delivered to the load
Substitute
Find the apparent power delivered to the load
Modify the expression in Equation (1) for the complex power supplied by the source as follows:
Substitute
Rewrite the expression for complex power supplied by the source in rectangular form as follows:
Compare the complex power supplied by the source with the expression in Equation (3) and write the average and reactive power supplied by the source as follows:
Substitute 4886.7899 W for
If the imaginary part of the complex power (reactive power) is positive value, then the load has lagging power factor. If the imaginary part is negative value, then the load has leading power factor.
As the imaginary part of the given complex power is negative value, the power factor is leading power factor.
Conclusion:
Thus, the apparent power delivered to
(b)
Find the apparent power delivered to each load in the circuit in Figure 11.45 in the textbook and power factor of the source.
(b)
Answer to Problem 43E
The apparent power delivered to
Explanation of Solution
Given data:
The impedance of the loads are given as follows:
Calculation:
Substitute
Substitute
From Equation (5), substitute
Simplify the expression as follows:
Substitute
Modify the expression in Equation (2) for the voltage across the load
Substitute
Modify the expression in Equation (1) for the complex power delivered to the load
Substitute
Find the apparent power delivered to the load
Modify the expression in Equation (2) for the voltage across the load
Substitute
Find the current through the load
Substitute
Modify the expression in Equation (1) for the complex power delivered to the load
Substitute
Find the apparent power delivered to the load
Modify the expression in Equation (2) for the voltage across the load
Substitute
Modify the expression in Equation (1) for the complex power delivered to the load
Substitute
Find the apparent power delivered to the load
Modify the expression in Equation (2) for the voltage across the load
Substitute
Modify the expression in Equation (1) for the complex power delivered to the load
Substitute
Find the apparent power delivered to the load
Modify the expression in Equation (1) for the complex power supplied by the source as follows:
Substitute
Rewrite the expression for complex power supplied by the source in rectangular form as follows:
Compare the complex power supplied by the source with the expression in Equation (3) and write the average and reactive power supplied by the source as follows:
Substitute
If the imaginary part of the complex power (reactive power) is positive value, then the load has lagging power factor. If the imaginary part is negative value, then the load has leading power factor.
As the imaginary part of the given complex power is negative value, the power factor is leading power factor.
Conclusion:
Thus, the apparent power delivered to
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Chapter 11 Solutions
Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
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