Answer:Iph=7A, IL=12.12A, P=65.65W, Q=1538.6VAR, Theta=87.55ْ

In summary, the problem involves three 0.1 H inductors connected in a delta configuration to a 220V/50Hz three phase AC network. Using the equations for inductive reactance and phase current, the phase current and line current values are determined to be 7 A and 12.12 A, respectively. The reactive power and total reactive power are then calculated to be 1538.6 VAR and 4615 VAR, respectively, and the phase angle is found to be 87.55 degrees. However, since a purely inductive load does not dissipate power, the real power is determined to be 0 W.
  • #1
JasonHathaway
115
0
Hi everyone,1. Homework Statement

Three inductors with 0.1 H each are delta connected to three phase ac newtork with 220V/50Hz. Determine Iph, IL, P, Q and Theta.

Homework Equations


Showed at the attempt.

The Attempt at a Solution


[/B]
XL=2*pi*f*L=31.4 ohms
Iph=Uph/XL=220/31.4=7 A
IL=1.73*7=12.12 A

Q=(Iph)^2 XL=Uph Iph sin(theta)

Since I don't have theta and I need to determine it in thte first place, I shall use he first law.
Q=(7)^2 31.4=1538.6 VAR
QT=3*Q=4615 VAR

Then, I shall substitute the value of Q in the second law to get theta.
sin^-1 (theta)=Q/Uph Iph=1538.6/220*7=87.55 ْ

P=Uph Iph cos(theta)=65.65 W
PT=3*P=196.95 W
 
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  • #2
Are you sure that you should be seeing real power being dissipated by a purely reactive load? You might want to reconsider what the phase angle must be for such a load.
 
  • #3
I found out that a purley inductor doesn't disspate any power, which leads to P=0. Thanks :)
 

Related to Answer:Iph=7A, IL=12.12A, P=65.65W, Q=1538.6VAR, Theta=87.55ْ

What do the variables Iph, IL, P, Q, and Theta represent?

Iph represents the input current, IL represents the load current, P represents power, Q represents reactive power, and Theta represents the phase angle.

What are the units for Iph, IL, P, Q, and Theta?

Iph and IL are measured in amperes (A), P is measured in watts (W), Q is measured in volt-amperes reactive (VAR), and Theta is measured in degrees (°).

How are Iph, IL, P, Q, and Theta related?

Iph and IL are directly related through the ratio of input and load currents, P is indirectly related to Iph and IL through the power factor (cos Theta), and Q is directly related to Iph, IL, and Theta through the equation Q = Iph * IL * tan Theta.

What is the significance of a high or low value for each variable?

A high value for Iph and IL could indicate a high current demand, which could lead to overheating or damage to the system. A high value for P represents a high power demand, which could lead to increased electricity costs. A high value for Q indicates a high amount of reactive power, which could cause issues with voltage stability. A high value for Theta indicates a large phase difference between Iph and IL, which could lead to power quality issues.

How can Iph, IL, P, Q, and Theta be measured or calculated?

Iph and IL can be measured with a current meter, P can be calculated using the equation P = Iph * IL * cos Theta, Q can be calculated using the equation Q = Iph * IL * tan Theta, and Theta can be measured with a phase meter or calculated using the equation Theta = arctan(Q/(Iph * IL)).

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