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• Notes

$\begin{array}{l}{\text { a) For the circuit shown, use the node-voltage method to find } V_{l}, V_{2} \text { , and } i .} \\ {\text { b) How much power is delivered to the circuit by the } 15 \text { A source? }} \\ {\text { c) Repeat }(b) \text { for the } 5 \text { A source. }}\end{array}$

$\text { Node Voltage Method }$

خطوات الحل

(1) ref. node

(2) تحدد باقي $V_{1}, V_{2},V_{3}, \text { nodes }$

(3)

$\text { node (1) }$

$\left(\sum \frac{1}{R_{1}}\right) V_{1}-\frac{1}{R_{12}} V_{2}-\frac{1}{R_{13}} V_{3}=I_{in})$

المصادر

$\text {node(2)}$

$\left(\sum \frac{1}{R_{2}}\right) V_{2}-\frac{1}{R_{21}} V_{1}-\frac{1}{R_{23}}=V_{3}=I_{in})$

$\text { node (1)} \ V_1$

$\left(\frac{1}{5}+\frac{1}{15}+\frac{1}{60}\right) V_{1}-\frac{1}{5} V_2=15 \longrightarrow (1)$

$\text {node (2)} \ V_{2}$

$\left(\frac{1}{5}+\frac{1}{2}\right) V_{2}-\frac{1}{5} V_1=-5 \longrightarrow (2)$

solve (1), (2) $V_{1}=60 V , V_2=10 V$

$i_1=\frac{V_{1}-V_{2}}{5}=\frac{60-10}{5}=10A$

$P_{15A}=-{VI}=-60*15=900w$

$P_{5 A}=V I=10*5=50w$