Find a Thevenin equivalent circuit to represent the resistive network below betw

Question

Find a Thevenin equivalent circuit to represent the resistive network below between terminalsa and b:

Explanation / Answer

for finding the equivalent thevinins resistance the voltage source should be shorted and the current source is open circuited. => 2 and 2 ohms become in series => 4 ohms and 3 and 6 ohms becomes in series=>9 ohms now 4 and 9 are in parallel => 4*9/13 =2.78 ohms by applying nodal analysis let V1 be the node voltage at voltage source V2 near current source V3 near 3 ohm KCL at node 2 (V1-V2)/2+10 = V2/2 ................1 at node 1 (V1-V3)/3 +(V1-V2)/2 =0.............2 at node 3 10+(V1-V3)/2 +V3/6 = 0...............3 solving V1=60 V2=40 V3=90 so Vthevinin = Vab = 10+60 = 70 V and Rth as already calculated Rth = 2.78 ohms

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