$(37$ points$)$ Consider the circuit shown below

fI

$($a$)$ Write down the general case of Kirchhoff's Rules in mathematical form

$21$

$x_{V_1-I_1{R}_1-I_2{R}_2}=0+2$

$(iti)$

$V_2-I_1{R}_1-I_3{A}_3=0$

$I_1+I_2=I_3$

${\displaystyle \underset{i}{\overset{?}{}}}{V}_i=0$

more genend

$($b$)$ Use Kirchhoff's Rules to find the resistance $R_2$ in terms of the variables $V_1,V_2,R_1,I_3,$ given in the diagram. $+2$

$($a$)$