Calculating Wattmeter Readings in a Three-Wire System with a Balanced Load

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In summary, the problem involves finding the wattmeter readings in a three-wire 173.2 volt CBA system with a balanced load. The line current Ia is given as 32.7 with an angle of -41.9. Using the equations Wb= Vba Ib cos ( angle between Vba and Ib) and Wc= Vca Ic cos (angle between Vca and Ic), the wattmeter readings are found to be Wb= -1167.87 w and Wc= 4215.5 w. However, the book's answer is Wb= 1170 W and Wc= 5370 W, which does not match. The issue may lie in the angle
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Homework Statement


Wattmeters are in the lines B and C of a three-wire, 173.2 volt, CBA system which supplies a balanced load. Find the wattmeter readings if line current Ia= 32.7 angle of (-41.9). Answer: 1170, 5370 w


Homework Equations


Wb= Vba Ib cos ( angle between Vba and Ib)
Wc= Vca Ic cos (angle between Vca and Ic)
Wb+Wc = 3 phase power
Wc-Wb = 3 phase reactive power


The Attempt at a Solution


I have solve for Vba , Vca Ic and Ib by phasor method..
Wb = (173.2 ) (32.7) cos ( 180- 78.1)
Wb= - 1167.87 w
Wc= (173.2) (32.7) cos (161.9 - 120)
Wc= 4215.5 w
my problem is when i checked my answer on the book my answers are not like in the book..
 
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book answer is Wb= 1170 W, Wc= 5370 W i can't figure out where i went wrong.. please help me to solve this problem
 

Related to Calculating Wattmeter Readings in a Three-Wire System with a Balanced Load

1. What is the Two Wattmeter Method?

The Two Wattmeter Method is a technique used in three-phase power systems to measure the power consumption of a load. It involves using two wattmeters to measure the voltage and current of each phase, and then using mathematical equations to calculate the total power consumption.

2. Why is the Two Wattmeter Method used instead of the Single Wattmeter Method?

The Two Wattmeter Method is used because it is more accurate in measuring the power consumption of a load in a three-phase power system. The Single Wattmeter Method only measures the power in one phase and assumes that the other two phases are balanced, which may not always be the case.

3. How is the power factor calculated using the Two Wattmeter Method?

The power factor is calculated by dividing the difference between the readings of the two wattmeters by the sum of the readings. This value is then multiplied by the cosine of the phase angle between the voltage and current of the load.

4. Can the Two Wattmeter Method be used for unbalanced three-phase loads?

Yes, the Two Wattmeter Method can be used for both balanced and unbalanced three-phase loads. However, for unbalanced loads, the power factor calculation becomes more complex and may require additional measurements.

5. What are the advantages of using the Two Wattmeter Method?

The Two Wattmeter Method offers several advantages, such as higher accuracy, ability to measure unbalanced loads, and the ability to calculate power factor for non-linear loads. It also requires fewer measurements compared to other methods, making it more efficient and cost-effective.

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