$($a$)(15$ points$)$ Find the three currents I$1,12$ and $13$ in the figure above, and clearly indicate their directions on the figure.

$($b$)(5$ points$)$ What is power of battery with $4$ V EMF $?$ Clearly state if the battery supplying energy or absorbing$.$

$($c$)(10$ points$)$ What is energy dissipation of the $2$ Ohm resistor during $1$ hr of operation.