The problems about power factor changed in RCL circuit, help~

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Discussion Overview

The discussion revolves around the calculations and implications of power factor changes in an RCL circuit. Participants explore the effects of adding a capacitor to the circuit, analyzing the resulting power factor and discrepancies in calculated values using different methods. The scope includes theoretical calculations and practical implications in circuit design.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents calculations for an RCL circuit with given values, questioning the differences in results when using two methods to find the required capacitance.
  • Another participant confirms the calculations for the initial circuit configuration but asks for clarification on the component values and conditions for the modified circuit.
  • It is noted that the components remain the same when adding the capacitor to change the power factor from 1 to 0.8.
  • A participant suggests that knowing the power factor and resistance allows for the calculation of the corresponding reactance, indicating a potential method for finding the required capacitance.
  • Multiple participants express confusion over differing results from various methods of calculating reactance and power factor, particularly regarding the sign of reactive power when the power factor is leading.
  • Concerns are raised about the accuracy of impedance values and their impact on calculations, with one participant suggesting that the magnitude of the impedance should be derivable from the known resistance and power factor.

Areas of Agreement / Disagreement

Participants generally agree on the initial calculations for the circuit but express differing views on the methods used to calculate the required capacitance and the implications of power factor changes. The discussion remains unresolved regarding the discrepancies in results and the correct approach to the calculations.

Contextual Notes

Participants highlight potential limitations in their calculations, including assumptions about the circuit configuration and the definitions of reactive power. There is an ongoing uncertainty about the correct interpretation of the power factor and its effects on the circuit.

qpzm77gg
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R = 100Ω, L=0.5H, supply voltage vs(t) = 12sin(377t) in Figure 1a

XL = wL =377(0.5) = 188.5Ω
vrms = 8.485∠0
Z=213.38∠62.05 Ω
I = 8.485∠0/ 213.38∠62.05 = 0.0398∠-62.05 A
VR = 3.98∠-62.05 V
VL = 7.502∠27.95 V
PT = 0.03982(100) = 0.158W
QT = QL = 0.299 VAR
ST = 0.338∠62.05 VA
Fp = 0.467a capacitor is added to the circuit in series in figure 1b, and Fp = 1
S=0.158∠0
Q=0
PT=0.0346W
I=0.0186A
Z=455.7Ω
C=14.1μF

If Fp in figure 1b is equal to 0.8
Q=0.02595VAR(ind)
I=0.0051∠36.87 A
Z=1662.82∠-36.87 Ω

For the capacitance of here, I'm so interrogative.

If I used the method of QT =QL - Qc
Qc = 0.0049-0.02595 = -0.02105VAR
Xc=809.3Ω
But I used the method of Vs=Vc+VR+VL
Vc = 8.485-0.0051(100)-0.0051(188.5)=7.01V
Xc=1374.5Ω

Why the answers are different when I used these two methods, and it's correct all of my above answers? If some are wrong, please feel free to indicated the mistake. The Figure 1a and 1b are uploaded the files.
Thanks
 

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Your calculations for the required capacitor in Figure (a) appear to be fine.

For Figure (b), what are the given component values and conditions? Are the voltage source, resistance, and inductance the same as before?
 
gneill said:
Your calculations for the required capacitor in Figure (a) appear to be fine.

For Figure (b), what are the given component values and conditions? Are the voltage source, resistance, and inductance the same as before?


Yes, They are same as before, and then step and step add the capacitor in the circuit and change the power factor from 1 to 0.8.
Thanks
 
qpzm77gg said:
Yes, They are same as before, and then step and step add the capacitor in the circuit and change the power factor from 1 to 0.8.
Thanks

Just to be clear, the components start out as Vs, R, L, and C from part (a) where the power factor is 1, and you wish to add another capacitor to bring the power factor down to 0.8?
 
gneill said:
Just to be clear, the components start out as Vs, R, L, and C from part (a) where the power factor is 1, and you wish to add another capacitor to bring the power factor down to 0.8?

The complete question is uploaded in the file.
Thanks a lot.
 

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Okay. Having the complete question helps.

For part (c)(iv), finding the capacitance, if you know the power factor and the resistance (the real part of the impedance), then you should be able to find the corresponding reactance. After all,
$$ pf = cos(\theta) = \frac{R}{\sqrt{R^2 + X^2}}$$
X will be positive or negative depending upon whether the current is said to be lagging or leading. You can then find XC from X = XL + XC.

I haven't been able to follow how you've approached parts (i) through (iii). I think if it were me I would have been tempted to do the parts in reverse order :smile:
 
QT = QL-Qc
Because all I are same in the in series circuit.
XT=XL - Xc
QT/I2=188.5-Xc
Xc = 1186.19Ω

another method,
|Z|=1662.82
|Z|2 = R2+Xc22
1662.822 = 1002+Xc22
Xc2=1659.8Ω
QT=I2(1659.8)
QT=0.0432VAR(cap)
Qc=QL-QT
Qc=0.0049+0.0432=0.0481VAR(cap)
Xc=0.0481/0.00512=1849.3Ω


There are also difference between the answers, why?
 
qpzm77gg said:
QT = QL-Qc
Because all I are same in the in series circuit.
XT=XL - Xc
QT/I2=188.5-Xc
Xc = 1186.19Ω
Is Q a positive or negative value if the pf is leading?
another method,
|Z|=1662.82
|Z|2 = R2+Xc22
1662.822 = 1002+Xc22
Xc2=1659.8Ω
QT=I2(1659.8)
QT=0.0432VAR(cap)
Qc=QL-QT
Qc=0.0049+0.0432=0.0481VAR(cap)
Xc=0.0481/0.00512=1849.3Ω


There are also difference between the answers, why?

I have suspicions about your value for the impedance. Since you know the real part R is 100 Ohms, you should be able to find the magnitude of the impedance given the power factor. You should also be able to find the magnitude of the reactive part.