3. (a) In the magnetic circuit shown in Figure Q3(a), the steel core has a relative permeability of 1200. The dimensions of each section of the circuit are labeled in Figure Q3(a), in the unit of centimeters. The core has a square cross-sectional area. Two connected 500-turn coils are wound on the steel core as illustrated, with 10 A current flowing through the coils in the arrow direction. An air gap of 0.5 cm is at the center of the steel core as illustrated. Determine the air gap flux, the air gap flux density, and the magnetic field intensity in the air gap. (12 marks) 10 A 50 11 2 50 427 N1 50 0.5 500 turns N2 500 turns Figure Q3(a) (b) The following data were obtained when a down transformer rated as 20 kVA, 60 Hz, HV voltage 2400 V, HV current 8.33 A, LV voltage 240 V and LV current 83.3 A was tested using 60 Hz AC supply: When the HV winding is open-circuited and 240 V (rated LV voltage) is applied on the LV winding, 1.038 A current and 122 W power are measured at the LV winding; When the LV winding is short-circuited and 8.33 A (rated HV current) is measured on the HV winding, the HV voltage is 61.3 V and the power is 257 W. What is the efficiency at rated full-load current under normal working at 0.8 power factor? (8 marks)