The circuit in Fig. $1$ shows a basic setup with diodes. The voltage source originally has a DC offset $V_{dc}=0V$ and peak$-$to$-$peak voltage $V_{pp}$

Figure $1$: Problem $1$

$($i$)$ Write a piecewise expression for the current through $R_1$ if $V_{pp}=10V.$ Hint: Rather than write the function piecewise in time, you may write it piecewise with respect to the value of the voltage source.

$($ii$)$ Write an expression for the current through $R_1$ if $V_{dc}=1\mathrm{.}4V.$

$($iii$)$ Write an expression for the current through $R_1$ if $V_{dc}=-1\mathrm{.}4V.$

$($iv$)$ If the diodes were ideal with $V_{\text{t}\text{h}\text{r}\text{e}\text{s}\text{h}\text{o}\text{l}\text{d}}=0V,$ how does the circuit behavior change?

$($i$)$ Repeat Problem $1($all parts$)$ for the circuit in Fig. $2$

Figure $2$: Problem $2$