Concept explainers
(a) Find both wattmeter readings in Fig. 12.39 if VA = 100∠0 ° V rms, VB = 50∠90° V rms, ZA = 10 − j10 Ω, ZB = 8 + j6 Ω, and ZC = 30 + j10 Ω. (b) Is the sum of these readings equal to the total power taken by the three loads? Verify your answer with an appropriate simulation.
■ FIGURE 12.39
a.
Find the wattmeter readings in the circuit of Figure 12.39.
Answer to Problem 39E
The reading of wattmeter
Explanation of Solution
Given data:
The load impedance are
Calculation:
The given figure with mesh currents is shown in Figure 1.
Apply Kirchhoff’s voltage law to the loop with current
Apply Kirchhoff’s voltage law to the loop with current
Apply Kirchhoff’s voltage law to the loop with current
Rearrange equation (1).
Substitute equation (4) in (3).
Simplify the equation as follows.
Substitute equation (5) in (4).
Substitute equation (6) in (2).
Simplify the equation as follows.
Substitute
Substitute
Calculate the power delivered by phase A as follows.
Calculate the power delivered by phase B as follows.
Conclusion:
Thus, the reading of wattmeter
b.
Verify that the sum of the wattmeter reading is equal to the total power taken by the three loads using LTspice.
Explanation of Solution
Formula used:
Write the expression for inductive reactance.
Here,
Write the expression for capacitive reactance.
Here,
Calculation:
Let us assume that the angular frequency
Substitute
Substitute
Substitute
LTspice Simulation:
Draw the given figure in LTspice as shown in Figure 2. V1 zero and V2 zero connected in the circuit to find the current flows through it.
Set the values of voltages VA by right clicking on the voltage component, select none in “Functions” and enter the Small signal AC analysis parameters: AC amplitude as 100 for V1 as shown in Figure 3 for VA.
Now save the circuit, and open the “Edit Simulation command” choose AC analysis and select the sweep type as Decade, Number of points per decade 1, Start frequency and Stop frequency as 0.159155 Hz.
Now, run the simulation for the designed circuit. The output for the AC analysis will displays as shown in Figure 5.
From above simulation results, the current flows through the load resistance are given below.
Calculate the power delivered to load
Calculate the power delivered to load
Calculate the power delivered to load
The total power delivered to the load is
The sum of the wattmeter reading is
Conclusion:
Thus, it is verified that sum of the wattmeter reading is equal to the total power taken by the three loads using LTspice.
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Chapter 12 Solutions
Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
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