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

$$
\text { Node Voltage Method }
$$

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) $$
V_{1}=60 V , V_2=10 V
$$

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

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

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

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