- #1
JosefMTD
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Homework Statement
f = 60 Hz
pf = 0.8 (lagging)
Homework Equations
Z(L) = 2 (pi) * f * L
Given z = x + iy
tan(angle) = y/x
pf = cos(angle)
The Attempt at a Solution
I changed the Wye-connected resistors to an equivalent Delta-connected resistors:
The new resistors become 3R in the equivalent Delta-connected resistors
Next step is calculating Z(L)
Z(L) = j*2 (pi) * 60 Hz * 2 H = 754j ohm
1/Zphase = 1/Z(L) + 1/Z(R)
1/Zphase = 1/754j ohm + 1/3R ohm = -j/754 ohm + 1/3R ohm
1/Zphase = (754 ohm - 3Rj)/754 ohm*3R ohm
Since V is not given value in this problem, I choose to use an arbitrary value of x with angle of 0 degree, thus making it a constant.
Iphase = Vphase/Zphase = x*(754 ohm -3Rj)/754 ohm*3R ohm
It's known that power factor is 0.8
cos(angle) = 0.8
angle = arc cos(0.8) = +/- 37
Since known that the current is lagging, the angle is lower than 0 degree, thus making the appropriate angle is -37 degree.
Since I know the angle of phase I, I put it in the formula to find the angle of a complex number:
tan(angle) = Im(complex variable)/Re(complex variable)
tan(-37 degree) = [(x/754 ohm*3R)(-3Rj)]/[(x/754 ohm*3R)(754)] = -3R / 754
- 0.75 = -3R / 754
R = 754/4 Ohm = 188.5 ohm
Am I doing it right?
Thank you in advance for helping me to solve this!