A 4-pole DC motor has a lap-connected armature winding. The flux per pole is 30 mWb and the total number of armature conductors is 250. When connected to a DC supply of 230 V, it draws an armature current of 40 A. Assuming an armature resistance of 0.6 Ω, calculate the back EMF.

A star-connected, 3-phase, 10 MVA, 6.6 kV alternator is protected by circulating current protection, with the star point being earthed via a resistance r. Estimate the value of earthing resistance if 85% of the stator winding is protected against earth faults. Assume an earth fault setting of 20%. Neglect the impedance of the alternator winding.

Calculate the active power (P) in a balanced three-phase delta-connected system with line voltage VL = 400 V, line current IL = 10 A, and power factor cos(φ) = 0.8.