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My teacher did the norton's equivalent in the class, and now for studying purposes i was trying to get to the Thévenin's one. However it seems my equations are somehow wrong, and i can't figure out why.

The Eq resistance is 8||2, which is 1.6 ohms.

I tried to apply Nodal analysis first

so,

for node V1: [tex]\frac{20-V_1}{3}=\frac{V_1-V_3}{2}[/tex]

for node V2: [tex]\frac{V_1-V_3}{2}=6+\frac{V_2-0}{5}=[/tex]

The relationship between two voltages is also known, which is [tex]V_2=V_3+10[/tex]

which gives V1=2 ; V2=0 ; V3=-10.

V1-V2 should indeed be 2, because from my teachers resolution, Vab = 2V. I don't get is how can V2 be 0? Then there can't be another voltage drop when it reaches the ground (0V)

Also, then i tried mesh analysis:

For mesh 1[tex]20+10=3I_1+2I_1+5(I_1+I_2)[/tex]

For mesh 2 [tex]0=5(I_2-I_1)+v[/tex]

[tex]I_2=6[/tex]

Where v is the voltage drop across the current source.

It gives I1 = 6 and v (which is equal to the V2 of the nodal analysis) = 0 again.

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# Thévenin's Equivalent Circuit

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