Admittance Circuit Homework: Improve PF to Unity & Reduce Supply Curr.

[DT71]

Homework Statement

A factory’s electrical load can be represented as three parallel
admittances, as shown in FIGURE 1. The values of the admittances are
given in the table in polar form.
(a) Determine
(i) the current taken from the supply
(ii) the overall power factor of the load
(iii) the value of the capacitor required in parallel to the load to
reduce the supply current by 20% and the new power factor
with the capacitor in circuit.
(b) The power factor for the factory load can be improved to unity by
using a sufficiently large parallel capacitor.
(i) Calculate the value of this capacitor.
(ii) Calculate the resonant frequency of the circuit when this
capacitor is in circuit. (Hint: using the condition that at
resonance BC = BL, like XC = XL in a series circuit, greatly
simplifies this calculation!) Comment on your answer.
(iii) State, with reasons, if the ‘unity power factor’ condition gives
the minimum value of supply current. (You could also
demonstrate this graphically using a spreadsheet.)

Homework Equations

The Attempt at a Solution

I have the following answers so far,
a)i)I=95L-46.30 degrees A
a)ii)p.f.=0.72
a)iii)C=775uF
this is were I am stuck...

 

[KataKoniK]

Thank you for your question. I have carefully examined your problem and have some suggestions for you to consider.

Firstly, in order to solve for the value of the capacitor required to reduce the supply current by 20% and the new power factor, it would be helpful to have more information about the frequency of the circuit. This information is necessary to calculate the reactance of the capacitor and its effect on the overall power factor. Additionally, it would be helpful to know the voltage and current of the supply in order to accurately calculate the power factor.

Secondly, in order to calculate the value of the capacitor needed to achieve unity power factor, we need to know the current and voltage of the supply, as well as the frequency of the circuit. Without this information, it is not possible to accurately determine the value of the capacitor.

Lastly, in order to determine if the unity power factor condition gives the minimum value of supply current, we would need to analyze the circuit at different power factors and compare the resulting supply currents. This can be done graphically using a spreadsheet, as you suggested, or by solving for the supply current at different power factors using the given admittances and the voltage and frequency of the circuit.

I hope these suggestions will help you in solving your problem. If you need further assistance, please do not hesitate to reach out. it is my job to help others understand and solve complex problems, and I am happy to assist you in any way I can.