$5.$ A buck converter, without a filter capacitor is driving a resistive load as in Figure $12\mathrm{.}61.$

Figure $12\mathrm{.}61$ Buck converter without filter capacitor

$($a$)$ The device is in steady state with a duty cycle $\backslash ($ D$=0\mathrm{.}5\backslash ).$ The switching frequency is $2$ kHz $.$ What is average output voltage?

$($b$)$ Calculate the maximum and minimum output voltage. Sketch the waveform.