Problem ecse 4080 f2019-fe-9 a boost converter has been designed to charge a battery string from a solar panel. the converter switching frequency is 12 khz. the nominal input is 15 v at up to 5 a, and the nominal output is 72 v. the inductor has value of 500 uh, and a 5 uf capacitor is connected in parallel with the battery string. the inductor's internal resistance is rl= 0.2 12. the transistor is a mosfet with rds(on) = 0.2 12. the diode can be modeled as a 0.5-v drop in series with forward resistance rp = 0.02 22. the total internal equivalent surge resistance (esr) of the battery string is rb = 2 12. use the inductor current and the capacitor voltage as state variables during each switching cycle. part a) (3 points): draw the circuit. part b) (2 points): since the output is a battery, should the capacitor voltage be included as a state variable? explain your answer. part c) (5 points): develop an averaged model for this circuit. part d) (5 points): develop the expression for the output voltage, v. = vc, as function of the duty ratio, d. part d) (5 points): determine the nominal (i. e., steady-state) operating point, dnom, for the given data. part e) (2 points): draw the curve of vo versus d for 0.65 5d=0.95. part f) (3 points): based on the graph in part e), is an upper limit on the operating duty ratio needed? suggests a maximum value for d.