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# Find the Node Voltages π½π,π½ππππ π½π and Current Through 0.5Ο - Basic Electrical and Electronics Engineering

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Sum

Find the node voltages π½π,π½π πππ π½π and current through 0.5Ω

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#### Solution

Applying KCL at node 1

-4+(V_1-V_2)/0.33+(V_1-V_2)/0.5=0

0.83π1−0.5π2−0.33π3=0.66 …..(1)

Applying KCL at node 2

V_2/0.2+V_2+5-V_3+(V_2-V_1)/0.33=0

−0.2π1+0.596π2−0.066π3=−0.33 …….(2)
Applying KCL at node 3

(V_3-V_1)/0.5+V_3+V_3-5-V_2=0

−π1−π2+2.5π3=5 ………(3)
From (1), (2) and (3) we get,
π1=2.46π       π2=0.63π       π3=3.23π
Applying KCL,

I=(V_1-V_3)/0.5=(2.46-3.23)/0.5

I = −1.54π΄π π(π.πΩ)= π.ππππ¦(←)

Concept: Three Phase Voltage Genration
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