CircuitThevenin and Norton Equivalents Problems 1

$$
\begin{array}{l}{\text { Find the Thévenin equivalent circuit with respect }} \\ {\text { to the terminals a, b for the circuit shown. }}\end{array}
$$

خطوات الحل

Thévenin

(1) $$O.C$$

(2) $$R_{th}$$

(3) 

(4) 

(2) RA

$$
R_{eq}=\frac{5 * 20}{20+5}=4 \Omega
$$

$$
R_{eq}=\frac{R}{2}=\frac{12}{2}=6 \Omega
$$

$$V_{th}$$

node (1)

$$
(\sum \frac{1}{R_{1}}) V_{1}-\frac{1}{R_{12}}V_2-\frac{1}{R_{13}}V_3=I
$$

$$
\left(\frac{1}{5}+\frac{1}{8}+\frac{1}{20}\right) V_{1}-\frac{1}{8}V_{th}-\frac{1}{5}*72=0 \longrightarrow (1)
$$

$$
\left(\frac{1}{8}+\frac{1}{12}\right)V_{th}-\frac{1}{12}*72-\frac{V_1}{8}=0 \longrightarrow (2)
$$

Solve (1), (2)     $$
V_{1}=60 V
$$        $$
V_{t h}=64.8 V
$$

$$
R_{th}=6 \Omega
$$

$$
V_{th}=
$$