Find the complex power absorbed by each passive element in the circuit in Figure 11.47 in the textbook and power factor of the source.
Answer to Problem 48E
The complex power absorbed by
Explanation of Solution
Given data:
Refer to Figure 11.47 in the textbook for the given circuit.
Formula used:
Write the expression for complex power absorbed by the element as follows:
Here,
Write the expression for current in terms of voltage 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:
Find the equivalent impedance of the shunt components in the circuit as follows:
Use the expression in Equation (2) and find the source current as follows:
Substitute
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.
Use voltage division rule and find the voltage across
Substitute
Modify the expression in Equation (1) for the complex power absorbed by the
Substitute
Consider the node voltage across the shunt branches as
Substitute
Use voltage division rule and find the voltage across
Substitute
Use current division rule and find the current through first shunt branch (through
Substitute
Modify the expression in Equation (1) for the complex power absorbed by the
Substitute
Use voltage division rule and find the voltage across
Substitute
Modify the expression in Equation (1) for the complex power absorbed by the
Substitute
Use current division rule and find the current through second shunt branch (through
Substitute
Modify the expression in Equation (1) for the complex power absorbed by the
Substitute
Use current division rule and find the current through third shunt branch (through
Substitute
Modify the expression in Equation (1) for the complex power absorbed by the
Substitute
Conclusion:
Thus, the complex power absorbed by
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