Question

The voltage and current of a y-connected load are vab= 25∠15◦ v, ic= 10∠75◦ a

a. Compute Vbaron b. Compute Ia c. Compute the power factor angle d. Compute the real power of the load

Answer 1

a. To compute Vb, we need to use the voltage divider formula. Vb = Vab * Zb / (Za + Zb + Zc), where Za, Zb, and Zc are the impedances of the three branches of the load. Since the load is Y-connected, we know that Za = Zb = Zc. Therefore, Vb = Vab / 2 = 12.5∠15◦ V.

b. To compute Ia, we can use the current divider formula. Ia = Ic * Zb / (Za + Zb + Zc), where Za, Zb, and Zc are the impedances of the three branches of the load. Since the load is Y-connected, we know that Za = Zb = Zc. Therefore, Ia = Ic / 3 = 3.33∠75◦ A.

c. The power factor angle is the angle between the voltage and current phasors. Therefore, the power factor angle is 15 - 75 = -60 degrees.

d. The real power of the load is given by P = Vb * Ia * cos(theta), where theta is the power factor angle. Therefore, P = 12.5 * 3.33 * cos(-60) = 21.65 W

Step-by-step explanation: