
Concept explainers
A regular household system of a single-phase three-wire circuit allows the operation of both 120-V and 240-V, 60-Hz appliances. The household circuit is modeled as shown in Fig. 11.96. Calculate:
- (a) the currents I1, I2, and In
- (b) the total complex power supplied
- (c) the overall power factor of the circuit
(a)

Find the currents
Explanation of Solution
Given data:
Refer to Figure 11.96 in the textbook.
The frequency
The circuits performs at both the voltages
The inductance L is
Formula used:
Write the expression for reactance of an inductor
Here,
L is the inductance.
Calculation:
Refer to Figure 11.96 in the textbook.
Substitute
The modified Figure is shown in Figure 1.
In Figure 1, the current flowing through the lamp
The current flowing through the refrigerator is calculated by using Ohm’s law as follows.
Convert the equation from polar to rectangular form.
The current flowing through the kitchen range
In Figure, apply Kirchhoff’s current law in the circuit. Therefore, the current
Similarly, the current
Convert the equation from rectangular to polar form.
Similarly, the current
Convert the equation from rectangular to polar form.
Conclusion:
Thus, the currents
(b)

Find the total complex power in the circuit of Figure 11.96.
Answer to Problem 85P
The total complex power is
Explanation of Solution
Given data:
Refer to Figure 11.96 in the textbook.
From part (a),
Calculation:
Refer to Figure 1 shown in Part (a).
The complex power delivered by the voltage source 1 is,
Substitute
The complex power delivered by voltage source 2 is,
Substitute
Simply the equation as follows,
Convert the equation from polar to rectangular form.
The total complex power is,
Substitute
Conclusion:
Thus, the total complex power is
(c)

Find the total power factor of the circuit shown in Figure 11.96.
Answer to Problem 85P
The total power factor of the circuit is 0.9888 (lagging).
Explanation of Solution
Given data:
Refer to Figure 11.96 in the textbook.
Formula used:
Write the expression for complex power.
Here,
P is the real power, and
Q is the reactive power.
Write the expression for power factor.
Calculation:
On comparing equation (2) and (3), the real power is,
From equation (2), the apparent power S is,
Substitute
Since,
Conclusion:
Thus, the total power factor of the circuit is 0.9888 (lagging).
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Chapter 11 Solutions
Fundamentals of Electric Circuits
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