Given the circuit below,

$1)$ How many branches are there in the circuit? $(5$ pts$)$

$2)$ How many essential nodes are there in the circuit? $(5$ pts$)$

$3)$ How many voltage sources are there in the circuit? $(5$ pts$)$

$4)$ Write the KCL for essential nodes to determine the node voltage for each essential

node. $($using nodal$-$voltage analysis$)(30$ pts$)$

$5)$ How many independent loops are there in the circuit? $(5$ pts$)$

$6)$ Determine the current for each independent mesh using mesh current analysis. $(30$ pts$)$

$7)$ What$$s the current i in the circuit? $(5$ pts$)$