Electrical Principles – Phasor diagram exercise
For the phasor diagram below, calculate the following if the supply frequency is 60Hz:
1) VS
2) The values of the components and draw the circuit
3) The phase angle between the supply voltage and the current
4) The Power factor (this is the cosine of the phase angle)
5) The real power dissipated
6) The reactive power
1)
VS = 1002 + 452 = 109.65V
2)
To calculate R we need to multiply the in phase current by the in
phase voltage 100/12 = 8.33Ω.
To calculate the inductance we need a value for the inductive
reactance XL. We can get this from the reactive Voltage divided by the
current.
XL = 45/12 = 3.75Ω
The circuit then looks like this:
3)
The phase angle is the angle between VS and the Current i.e. angle φ
This we can get from the ratio of the side lengths.
Tan φ = 45/100 therefore φ = Tan-1 45/100 = 24.22°
4)
Power factor is the Cosine of the angle between VS and the current.
Cos 24.22 = 0.911
5)
The real power is the product of In phase Voltage and Current
Power = 100 * 12 – 1200W or 1.2kW
6)
The Reactive VA is the product of Reactive Voltage and current
VA = 45 * 12 = 540 W