For the full$-$wave rectifier circuit in Fig. $4\mathrm{.}24($a$),$ show the following: $($a$)$ The output is zero for an angle of $2si{n}^{-1}(\frac{V_D}{V_s})$ centered around the zero$-$crossing points of the sine$-$wave input. $($b$)$ The average value $($dc component$)$ of $v_o$ is $V_o(\frac{2}{})V_{,}-V_D.($c$)$ The peak current through each diode is $\frac{V_s-V_D}{R}.$ Find the fraction $($percentage$)$ of each cycle during which $v_o>0,$ the value of $V_o,$ the peak diode current, and the value of PIV, all for the case in which $v_s$ is a $12-V($ rms $)$ sinusoid$,V_{D}0\mathrm{.}7V,$ and $R=100.$