$($a$)$ Draw the graf to represent the circuit given in Figure $1,($b$)$ obtain the fundamental cut set and

$($c$)$ fundamental loop equations associated with the tree branches $\{1,2,3,4\}.$

For the circuit given in Figure $2,($a$)$ calculate incidence matrix from KCL$.($b$)$ express the voltages of all two$-$terminal circuit elements in terms of the node voltages. $($c$)$ express the currents of all

two$-$terminal circuit elements in terms of the mesh currents.

For the circuit given in Figure $3,$ obtain the equation to analysis the circuit using Chord $($Line$)$

current method such that unknown variable is i$\_(2).$

For the circuit given in Figure $3,$ obtain the equation to analysis the circuit using Branch Voltages

method such that unknown variable is v$\_(4).$