Solve Admittance Circuit Homework: Current, PF, Capacitor

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In summary, to calculate the overall power factor and determine the value of the capacitor required to reduce the supply current by 20%, you will need to use the formulas p.f. = cosθ and Q = V^2 * C * sin(θ), respectively.
  • #1
DT71
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Homework Statement


A factory's electrical load can be represented as 3 parallel admittances. The values of the admittances are in polar form:Y1=0.05-30degS;Y2=0.07-60degS and Y3=0.1-45degS
a)determine
i)the current taken from the supply
ii)the overall p.f. 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 p.f. with the capacitor in circuit

Homework Equations


Y^2=G^2+B^2
phase angle=arctan(B/G)


The Attempt at a Solution


i) I have completed this and convinced its correct I=95-46.37deg Amps

ii)Can I use the 46.37 degrees to work out the overall p.f.?

iii)I=95 x 0.8=76 A
Y=I/V to obtain a new value for Y
Y^2=G^2+B^2 to obtain a new value for B, as G remains the same.

any assistance would be appreciated.
 
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  • #2


Hi there,

I can help you with your question. Here are my suggestions:

i) To calculate the overall power factor (p.f.), you will need to use the formula p.f. = cosθ, where θ is the angle of the current (46.37 degrees in this case). So, the overall p.f. would be cos(46.37) = 0.71.

ii) To calculate the value of the capacitor required in parallel to the load, you will need to use the formula Q = V^2 * C * sin(θ), where Q is the reactive power, V is the supply voltage, C is the capacitance, and θ is the angle of the current. In this case, Q = (95)^2 * C * sin(46.37) = 76.24 * C. You can rearrange this equation to solve for C, which will give you the value of the capacitor required.

iii) Once you have the value of the capacitor, you can use it to recalculate the overall p.f. using the formula p.f. = cosθ, where θ is the new angle of the current. This will give you the new p.f. with the capacitor in circuit.

I hope this helps! Let me know if you have any further questions.
 

1. What is admittance in a circuit?

Admittance is the measure of how easily an alternating current (AC) can flow through a circuit. It is the inverse of impedance and is measured in siemens (S).

2. How do I calculate admittance in a circuit?

To calculate admittance, you need to know the voltage and current values in the circuit. Admittance (Y) is equal to the complex conjugate of the ratio of voltage (V) to current (I): Y = V/I*.

3. What is the significance of admittance in a circuit?

Admittance is important in understanding the behavior of AC circuits. It helps to determine the power, current, and voltage in the circuit, as well as the phase relationships between them.

4. How does a capacitor affect admittance in a circuit?

A capacitor has a reactance value that affects the admittance in a circuit. As the frequency of the AC increases, the reactance decreases, resulting in an increase in admittance. This is because the capacitor allows more current to flow as the frequency increases.

5. How can I improve the power factor (PF) in a circuit?

The power factor is a measure of how efficiently a circuit uses the power it receives. A low PF can result in wasted energy and higher electricity bills. To improve the PF, you can add capacitors to the circuit to offset the reactive power, or you can use power factor correction techniques to adjust the current and voltage to be in phase.

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