$1.$ Build the circuit below in SPICE. This is a very simple model of the motor we explored in the $555-$timer lab. The voltage source $\backslash ($ V$\_\{$s$\}\backslash )$ generates a unipolar periodic pulse with period of $\backslash ($ T$=2\backslash )$ ms $,$ amplitude $\backslash ($ A$=12\backslash$mathrm$\{$~V$\}\backslash )$ and duty cycle $\backslash ($ D$=0\mathrm{.}2\backslash ).$ Set $\backslash (\backslash$mathrm$\{$R$\}1=\backslash$mathrm$\{$R$\}2=5\backslash$Omega $\backslash ).$

DC$0$AC $11$

a$.$ With L$1=100$ mH$,$ perform a Transient Analysis and plot the current in the inductor over several cycles of the periodic pulse signal. Make sure to omit the initial transient period from the plot. Estimate the average value of the current and the ripple from the plot. Submit a screen capture.

b$.$ Now change the value of L $1$ and observe how the ripple changes. Find the $\backslash (\backslash$mathrm$\{$L$1\}\backslash )$ required for the size of the ripple to be less than $\backslash (5\backslash \%\backslash )$ of the average current.

c$.$ Repeat parts $($a$)$ and $($b$)$ with the period of the source $\backslash ($ V$\_\{$S$\}\backslash )$ increased to $20$ ms $.$ Comment on the results. Submit a screen capture.