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$$
\begin{array}{l}{\text { Use the mesh-current method to find (a) the }} \\ {\text { power delivered by the } 80 \mathrm{V} \text { source to the cir- }} \\ {\text { cuit shown and }(b) \text { the power dissipated in the }} \\ {8 \Omega \text { resistor. }}\end{array}
$$

$$
\text { Mesh Current Method }
$$

خطوات الحل

(1) تحديد عدد ال Meshes

(2) نفرض تيارات

(3) نطبق العلاقات 

$$
Mesh (1)
$$

$$
\left(\sum R_{1}\right) I_{1}-R_12 I_2-R_13 I_3 \pm V_B=0
$$

$$
Mesh (2)
$$

$$
\left(\sum R_{2}\right) I_{2}-R_21 I_1-R_23 I_3 \pm V_B=0
$$

$$
I_1, I_2, I_3
$$

$$
Mesh (1)
$$

$$
(5+26)I_1-5I_2-26 I_{3}-80=0 \longrightarrow (1)
$$

$$
Mesh (2)
$$

$$
(30+90+5)I_2-5I_1-90 I_3=0 \longrightarrow (2)
$$

$$
Mesh (3)
$$

$$
(90+8+26) I_3-26I_3-90 I_2=0 \longrightarrow (3)
$$

solve (1), (2), (3) $$
I_{1}=5 \mathrm{A} \quad I_{2}=2 \mathrm{A} \quad I_{3}=2.5 \mathrm{A}
$$

$$
P_{80V}=-VI_1=-80*5=400w
$$

$$
P_{8 \Omega}=I_{3}^{2}R=(25)^2*8=50w
$$

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