a) To determine the magnitude and phase of each line current supplied by the source, we use Ohm's law (I = V/Z). Given that the phase voltage V = 240∠30° V and the impedance Z = 50∠25° Ω, we can calculate the current as follows: I = V/Z = 240∠30° / 50∠25° = 4.8∠5° A This is the phase current for phase A. Since it's a balanced star connection, the line current equals the phase current. Therefore, the line current for each phase is 4.8∠5° A. b) To determine the active power and the reactive power supplied by the source, we use the power formula P = √3 * VL * IL * cos(θ) for active power and Q = √3 * VL * IL * sin(θ) for reactive power. Given that the line voltage VL = √3 * phase voltage = √3 * 240 V = 415.69 V, the line current IL = 4.8 A, and the power factor cos(θ) = cos(25°) = 0.9063, we can calculate: P = √3 * 415.69 V * 4.8 A * 0.9063 = 2721.6 W And for reactive power, sin(θ) = sin(25°) = 0.4226, so: Q = √3 * 415.69 V * 4.8 A * 0.4226 = 1341.6 VAR c) To determine the reactive power requirement of each of the three capacitances to improve the power factor to 0.95 lag, we first need to calculate the new reactive power Q_new using the formula Q_new = P * tan(θ_new), where θ_new = cos^(-1)(0.95). Q_new = 2721.6 W * tan(cos^(-1)(0.95)) = 859.5 VAR The reactive power provided by the capacitors should be the difference between the original reactive power and the new reactive power, which is Q - Q_new = 1341.6 VAR - 859.5 VAR = 482.1 VAR. Since the capacitors are connected in star, the reactive power for each capacitor is 482.1 VAR / 3 = 160.7 VAR. ####