1. The problem statement, all variables and given/known data f = 60 Hz pf = 0.8 (lagging) 2. Relevant equations Z(L) = 2 (pi) * f * L Given z = x + iy tan(angle) = y/x pf = cos(angle) 3. 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!