Question

1). Calculate the current intensity $I_x$

2). Générateur de Thévenin entre les bornes 𝑎−𝑏

Answer 1

Solution

1). Calculate the current intensity $I_x$

Redraw the circuit for the ;opp analysis, 

Apply KCL at  node A.

$I_1+I_x =1.5I_x$

$I_1=0.5I_x$   (1)

Redraw the circuit for the ;opp analysis, 

Apply KVL in both mesh.

$-6-5I_1+3I_x+4I_x=0$

From equation (1) :

$-6-5(0.5I_x)+3I_x+4I_x=0$

$-6-2.5I_x+3I_x+4I_x=0$

$-6+4.5I_x=0$

$4.5I_x=6=>I_x=\frac{6}{4.5}=1.33A$

2). Générateur de Thévenin entre les bornes 𝑎−𝑏

For ${E}_{th}$

${E}_{th}=4I_x$

       $=4(\frac{6}{4.5})=5.33V$

To calculate ${I}_{sc}$ , short the terminal a-b , The circuit would be drawn as,

Apply KVL in large loop .

$-6-5I_1+3{I}_{sc}=0$

Form equation (1) :

$-6-5(0.5I_x)+3{I}_{sc}=0$

$-6-2.5{I}_{sc}+3{I}_{sc}=0$

$0.5{I}_{sc}=6=>{I}_{sc}=\frac{6}{0.5}=12A$

Now, calculate ${R}_{th}$

${R}_{th}=\frac{{E}_{th}}{{I}_{sc}}=\frac{5.33}{12}=0.44\Omega$

1). Thus, $I_x=1.33A$

2). Thus, ${E}_{th}=5.33V$ & ${R}_{th}=0.44\Omega$