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• Notes

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

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

$\text {at} V_1$

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

$\text {at} V_2$

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

$KVL$

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

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

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

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

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

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

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