An Electric Range top burner control adjusts the duty cycle of the current and voltage supplied to surface heating element as a function of the control's dial setting. The range controller operates from a 240 VRMS single phase supply and, for the purposes of this problem, the burner element resistance is considered constant at 24 W. (In actuality, the resistance of the metallic element would increase with its temperature) The burner control dial setting dictates the duty cycle, D, of the current and voltage applied to the burner. The duty cycle D is the ratio of the time the burner is on, ton, to its period, T = (ton + toff). Thus D = ton /T. The control dial setting and the percent duty cycle D are as follows, where the underscored terms are the legends inscribed on the dial:
OFF 0%, LOW 10%, 2 20%, 3 30%, . . . , 8 80%, 9 90%, HIGH 100%
A. Find: The RMS value of the burner current and burner Average Power as a function of the dial setting using the definitions of the RMS and Average Power and express each in equation form.
B. Plot: The RMS value of the burner current and the burner Average Power as a function of the dial setting using a period T of ten seconds.