
Concept explainers
Consider the power system shown in Fig. 11.90. Calculate:
- (a) the total complex power
- (b) the power factor
- (c) the parallel capacitance necessary to establish a unity power factor
(a)

Calculate the complex power of the circuit shown in Figure 11.90.
Answer to Problem 75P
The total complex power for the given circuit is
Explanation of Solution
Given data:
Refer to Figure 11.90 in the textbook.
The voltage
The capacitance C is
The inductance L is
Formula used:
Write the expression to find the complex power.
Here,
Write the expression to find the complex power.
Here,
Calculation:
Refer to figure 11.90 in the textbook.
Consider the impedance
Consider the impedance
Consider the impedance
Substitute
Substitute
Substitute
The total complex power is,
Substitute
Comparing the above equation with equation (1).
Hence, the total complex power is,
Conclusion:
Thus, the total complex power for the given circuit is
(b)

Find the power factor for the given circuit.
Answer to Problem 75P
The power factor for the given circuit is
Explanation of Solution
Given data:
The voltage
From Part (a),
The real power and the reactive power is,
Formula used:
Write the expression to find the power factor
Here,
Write the expression for phase angle
Calculation:
Substitute
Substitute
Conclusion:
Thus, the power factor for the given circuit is
(c)

Find the parallel capacitance value required to establish a unity power factor.
Answer to Problem 75P
The value of capacitance is
Explanation of Solution
Given data:
The voltage
Formula used:
Write the expression to find the value of the capacitance.
Here,
Calculation:
Consider the frequency is
From equation (3), the reactive power is,
Substitute
Simplify the equation as follows,
Conclusion:
Thus, the value of capacitance is
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Chapter 11 Solutions
Fundamentals of Electric Circuits
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