Concept explainers
Consider the single-phase three-wire system shown in Fig. 12.78. Find the current in the neutral wire and the complex power supplied by each source. Take Vs as a 220∠0°-V, 60-Hz source.
Figure 12.78
Calculate the complex power supplied by each source and the current passing through the neutral wire.
Answer to Problem 87CP
The current in the neutral wire is
Explanation of Solution
Given data:
Refer to Figure 12.78 in the textbook for a single phase three wire system.
The source voltage is
The supply frequency is
Formula used:
Write the expression to find the complex power
Here,
Write the expression to find the complex power
Here,
Write the expression to find the inductance reactance in ohms.
Here,
Write the expression to find the angular frequency.
Here,
Calculation:
Substitute
Substitute
Modify the given figure with the assumed current directions as shown in Figure.1.
Apply Kirchhoff’s voltage law to loop 1of current
Apply Kirchhoff’s voltage law to loop 2 of current
Apply Kirchhoff’s voltage law to loop 3 of current
Represent the equation (5) (6) and (7) in matrix form.
Obtain the value of determinants as follows.
Write the expression to find the currents,
Substitute
Substitute
Substitute
Substitute
Thus, the neutral current is
Substitute
Substitute
Conclusion:
Thus, the current in the neutral wire is
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Chapter 12 Solutions
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