$1.(45$ points$)$ In the circuit below use superposition and answer the following.

a$.(20$ points$)$ Briefly, explain how the superposition principle is applied to analyze electric circuits.

b$.(25$ points$)$ Fill the following table:

$\backslash$begin$\{$tabular$\}\{|$l$|$l$|$r$|$c$|\}$

$\backslash$hline Variable & Value & Units & Points $\backslash \backslash$

$\backslash$hline$\backslash ($ I x$^\{\backslash$prime$\}\backslash )($when only the $10$ V source is ON$)$ & & mA & $8\mathrm{.}3\backslash \backslash$

$\backslash$hline $\backslash (\backslash$mid x$^\{\backslash$prime $\backslash$prime$\}\backslash )($when only the $2$ mA source is ON$)$ & & mA & $8\mathrm{.}3\backslash \backslash$

$\backslash$hline Total Ix & & mA & $8\mathrm{.}4\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$