Find the Capacitance when given the Power Factor

In summary, the person is trying to solve for the capacitance of a capacitor using a phasor diagram, but they are having trouble understanding why the angle is not being substituted in for 135 degrees.
  • #1
jaus tail
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Homework Statement


upload_2018-1-25_10-45-12.png

w = 1 rad/s
power factor is 0.8 lag

Homework Equations


Using Phasor we can do

The Attempt at a Solution


upload_2018-1-25_10-45-2.png

Since pf = 0.8 lag. I source lags V source by 36.87 degrees.
Vc is voltage across Capacitor = Voltage across ( Resistor + inductor)
upload_2018-1-25_11-5-14.png


Solving this I get C = 0.5
But book says C = 0.125
I had actually solved this sum many weeks ago and got right answer then but I cannot find the book now and am struggling to solve again. Can anybody help me?
 

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  • #2
Your phasor diagram is correct, but it is difficult to get anything out of it.

Assume the source to be of 1V.
Draw the phasor parallelogram of currents whose one phasor is the current in the RL branch (known) and other side as the capacitor current (unknown). Then you can solve it using simple geometry. The answer is indeed 0.125F.
 
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  • #3
upload_2018-1-26_9-27-52.png

upload_2018-1-26_9-29-18.png

I also get 0.125 if I make this change above.
In circled part, if I take Ic angle as 0 degrees I get answer, but why should Ic angle be zero. Ir = | Ic/(square root 2) / C |at angle -135 degrees as per equation 1. So when I substitute Ir angle 0, shouldn't I substitute Ic/1.414 / C and the angle -135 degrees as well?
But I get right answer when I substitute only magnitude of Ir and not the angle in the KCL equation. Why?

I also get the right answer if I substitute in KCL equation: Ic angle 135 by 1.414 C Ir angle 135.
But shouldn't it be angle 135 + 135? I'm not able to understand why only magnitude should be substituted and not the phase angle from equation 1... to get the right answer?
 

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Last edited:
  • #4
Can somebody please explain this to me? Why in the red circled part above has the angle not been substituted? If I replace 135 with zero then I get the answer.
 
  • #5
Sorry for the late reply, I'd almost forgot about this thread.

In your working, why have you multiplied IR by √2? It seems you forgot to multiply Ic by √2 as well, since √2 should not appear in the equations as it is just a scaling factor and gets canceled out on both the sides.
I haven't checked your solution thoroughly, but this is probably why you are having trouble with phase angles (sin 135°=1/√2 and maybe it cancels the √2 in your voltage/current magnitude).

Anyways, I won't recommend this approach for GATE. I believe the phasor approach would be easier and quicker.
All the best!
 
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Related to Find the Capacitance when given the Power Factor

What is capacitance and how does it relate to power factor?

Capacitance refers to the ability of a system to store an electrical charge. In the context of power factor, capacitance is the measure of a system's ability to store electrical energy and release it back into the system. It is an important factor in determining the efficiency and stability of an electrical system.

How do you calculate capacitance when given the power factor?

To calculate capacitance when given the power factor, you can use the following formula: C = Q / (V x PF), where C is the capacitance in farads, Q is the reactive power in volt-amperes reactive (VAR), V is the voltage in volts, and PF is the power factor.

What is the significance of finding the capacitance when given the power factor?

Finding the capacitance when given the power factor allows you to determine the amount of reactive power in a system. This is important because reactive power can cause inefficiency and instability in an electrical system. By knowing the capacitance, you can make adjustments to improve the power factor and optimize the system's performance.

What are some common applications of finding capacitance when given the power factor?

One common application is in power factor correction, where capacitors are used to reduce the amount of reactive power in a system and improve the power factor. Another application is in designing and optimizing electrical systems, where knowing the capacitance can help ensure efficient and stable operation.

Are there any limitations to using capacitance to determine the power factor?

Yes, there are a few limitations. Capacitance alone cannot accurately determine the power factor as it is just one component of the equation. Other factors such as inductance and resistance also play a role in determining the power factor. Additionally, the power factor can vary depending on the type of load and the operating conditions of the system.

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