Consider the two sub$-$circuits shown above. The open circuit voltage of circuit $C$ containing ideal sources and resistors is measured at $V_{oc}=10V$ while the current though the short circuit passing through the terminals is $I_{sc}=2\mathrm{.}5A.$

For this problem, we wish to find the power supplied or consumed by circuit $C$ when the two circuits given above are connected together. We know that the power of the $2$ A current source is given as $P_{(ls)}=30W$ when the two sub$-$circuits have not been connected.

a$)$ First, find the value of the unknown voltage source $V_s$ for the circuit on the left when $P_{(s)}=30W.$ When finding $V_s$ assume that the circuit on the left has not been connected to circuit $C$ yet.

b$)$ Next, find the Thevenin Equivalent circuit for the circuit on the left. Use the value of $V_s$ that you found in part $($a$).$

c$)$ Next, find the Thevenin Equivalent circuit for circuit $C.$

d$)$ Connect the two equivalent sub$-$circuits together to form one circuit. Evaluate this circuit to predict $I_{op}$ and $V_{op}($the operating value of I and $V$ defined above$)$ when the two circuits are connected.

e$)$ Finally, find the signed power of circuit $C.$