Find capacitor require to correct 0.95 lagging system resonant frequency?

Question

Hi can someone give me a very basic answer to an electrical engineering question.
I‘m working on a question where for a single phase system, the voltage is 240v, f = 50Hz,
and load of 35Ω and 250mH,
I can't find the capacitor to correct 0.95 lagging system resonant frequency cause I don't know how to calculate the value of I.
I'm struggling to find any theory on this subject online that I can understand!

Answer 1

I believe you have resonance confused with power factor.



First find the reactance of the 250 mH inductance



XL = 2 * Pi * f * L

XL= 2 * 3,1416 * 50 * 0.250

XL = 78.54 ohms



The impedance of the circuit is

Z =Sqrt(R^2 + XL^2)

Z = Sqrt(35^2 + 78.54^2)

Z = 85.9858 ohms



The power factor of the existing circuit is

PF = R / Z

PF = 35 / 85.9858

PF = 0.407



The impedance of the circuit at 0.95 must be

Z = R / PF

Z = 35 / 0.95

Z = 36.842 ohms



This indicates the reactance of the improved circuit PF must be

XL = Sqrt (Z^2 - R^2)

XL = Sqrt(36.842^2 - 35^2)

XL = 11.5 ohms



This indicates the capacitive reactance XC must be

Original XL - Improved PF XL = 85.9858 - 11.5 = 74.3858 ohms



using the formula

C = 1 / (2 * Pi * f * XC)

C = 1 /(2 * 3.1416 * 50 * 74.3858 )

C = 0.00004279 farads (Answer)





EDIT

I just answered the same question for another asker. He wanted ther resonant frequency at 0.95 PF. If you need it also, this is it.



The formula for the resonance frequency (PF = 0.95) is

f = 1 / (2 * Pi * Sqrt(L * C))

f = 1 / (2 * 3.1416 * Sqrt (0,25 * 0.00004279 ))

f = 48.66 hz



I suggest you check my calculations, Did them in a hurry.



EDIT

There is an error in the XL calculation. This means you will have to recalculate the answers. However, the method is correct



XL = 2 * Pi * f * L

XL= 2 * 3,1416 * 50 * 0.250

XL = 113.0976 ohms



XL is really 78.54



Last Edit

I have corrected the answer above, using the correct value for XL

TexMav

Answer 2

Hi can someone give me a very basic answer to an electrical engineering question.

I‘m working on a question where for a single phase system, the voltage is 240v, f = 50Hz,

and load of 35Ω and 250mH,

I can't find the capacitor to correct 0.95 lagging system resonant frequency cause I don't know how to calculate the value of I.

I'm struggling to find any theory on this subject online that I can understand!

I = e/z

Z = 35ohms +J2*pi*50*0.25 = 35+J 78.5 = 86 at angle arctan78.5/35= 66 degrees

Answer 3

2πf = 1/√(LC)



√(LC) = 1/(2πf )



LC = 1/(2πf )^2



0.25C = 1/π^2 x 10^4



C = 4/π^2 x 10^4



C = 40 μF



"Lagging resonant frequency" is meaningless. You need to learn the words. Here is a free course: http://www.phy.davidson.edu/instrumentation/NEETS.htm