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$$
\begin{array}{l}{\text { a) Use the node-voltage method to find the }} \\ {\text { power associated with each source in the }} \\ {\text { circuit shown. }}\end{array}
$$

$$
\begin{array}{l}{\text { b) State whether the source is delivering power }} \\ {\text { to the circuit or extracting power from the }} \\ {\text { circuit. }}\end{array}
$$

$$
\text {at}   V_1
$$

$$
\left[\frac{1}{2}+\frac{1}{8}+\frac{1}{6}\right] V_{1}-\frac{1}{2} V_2=3i_1+\frac{50}{6}\longrightarrow (1)
$$

$$
\text {at} V_2
$$

$$
\left[\frac{1}{2}+\frac{1}{4}\right] V_{2}-\frac{1}{2} V_1=5-3i_1\longrightarrow (2)
$$

$$
 KVL
$$

$$
-50+6 i_1+V=0\longrightarrow (3)
$$

$$
V_1=32V
$$        $$
V_2=16 V
$$        $$
i_{1}=3 A
$$

$$
P_{50 V}=-V I=-50 * 3=-150w
$$
 $$
\text { generated } \Rightarrow \text { deliver. }
$$

$$
P_{5 A}=-V I=-5 *16=-80w
$$
 $$
\text { generated } \Rightarrow \text { deliver. }
$$

$$
V_{b a}=V_{12}=V_{1}-V_{2}
$$

$$
V_{b a}=32-16=16 v
$$

$$
P_{3 i_{1}}=-V I=-16*3i_1=-16*3*3=-144w
$$
 $$
\text { generated power } \Rightarrow \text { deliver. }
$$

 

 

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