Concept explainers
The single-phase three-wire system of Fig. 12.31 has three separate load impedances. If the source is balanced and Van = 110 +j0 V rms, (a) express Van and Vbn in phasor notation. (b) Determine the phasor voltage which appears across the impedance Z3. (c) Determine the average power delivered by the two sources if Z1 = 50 + j0 Ω, Z2 = 100 + j45 Ω, and Z3 = 100 – j90 Ω. (d) Represent load Z3 by a series connection of two elements, and state their respective values if the sources operate at 60 Hz.
(a)
The expression of phase to neutral voltage of phase
Answer to Problem 11E
The expression of phase to neutral voltage of phase
Explanation of Solution
Given data:
The phase to neutral voltage of phase
Calculation:
The given diagram is shown in Figure 1.
The general expression for the phasor notation is given by,
Here,
The magnitude of
Here,
The angle measured from the reference
Substitute
Substitute
Substitute
The voltage
The voltage
Substitute
Substitute
Conclusion:
Therefore, the expression of phase to neutral voltage of phase
(b)
The phasor voltage which appears across the impedance
Answer to Problem 11E
The phasor voltage which appears across the impedance
Explanation of Solution
Calculation:
The voltage across the impedance
The voltage across the impedance
The voltage across the impedance
The voltage across the impedance
Substitute
Conclusion:
Therefore, the phasor voltage which appears across the impedance
(c)
The average power delivered by the two sources.
Answer to Problem 11E
The average power delivered by source
Explanation of Solution
Given data:
The value of the impedance
The value of the impedance
The value of the impedance
Calculation:
The required diagram is shown in Figure 2.
The formula to find current
Substitute
Substitute
Substitute
Substitute
The formula to find current
Substitute
Substitute
Substitute
Substitute
The formula to find current
Substitute
The power
Substitute
The power
Substitute
Conclusion:
Therefore, the average power delivered by source
(d)
The representation of load
Answer to Problem 11E
The impedance
Explanation of Solution
Given data:
The operating frequency is
Calculation:
The value of the impedance
The real part of
Hence, the resistance
The imaginary part of
Hence, The series capacitive reactance
Here,
Substitute
Conclusion:
Therefore, the impedance
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Chapter 12 Solutions
Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
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