Question

A star-connected balanced load is supplied from a 3− φ balanced supply with a line voltage of 416 volts at a frequency of 50 Hz. Each phase of the load consists of a resistance and a capacitor joined in series and the reading on two wattmeters connected to measure the total power supplied are 782 W and 1980 W, both positive. Calculate (i) power factor of circuit, (ii) the line current, (iii) the capacitance of each capacitor

Answer 1

(i) tanφ = - (√3(W₁ - W₂))/(W₁ + W₂) = -(√3(782 - 1980))/(782 + 1980) = 0.75;

φ = 36.9°, cosφ = 0.8

(ii) 3 x 416 x I_L x 0.8 = 2762, I_L = 4.8A

(iii) Z_ph = V_ph/I_ph = (416√3)/4.8 = 50Ω; X_C = Z_phsinφ = 50 x 0.6 = 30Ω

Now, X_C = 1/2πfC = 1/2φ x 50 x C = 106 x 10^-6F