1. A 220 V, 50 Hz, 2-pulse, full wave, single-phase to three-phase cycloconverter is used to control an induction motor as reversible drive in the frequency range from 1 Hz to 6 Hz with constant torque control. If at particular operating condition load power factor is 0.88 and input displacement factor 0.70 then calculate (a) range of firing angle control, (b) highest value of input power factor and corresponding firing angle, (c) lowest value of input power factor and corresponding firing angle, (d) highest values of distortion factor and the its instant, (e) lowest values of distortion factor and the its instant.
2. 1 kW heating element of a 230 V, 50 Hz electric stove is to be controlled by a triac circuit. The gate circuit of the triac uses a 0.2 mF capacitor and a diac with a break over voltage of 50 V. Calculate the adjustable resistance value to provide control down to an rms voltage of 40 V.