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Find the Node Voltages π‘½πŸ,π‘½πŸπ’‚π’π’… π‘½πŸ‘ and Current Through 0.5Ο‰ - Basic Electrical and Electronics Engineering

Sum

Find the node voltages π‘½πŸ,π‘½πŸ 𝒂𝒏𝒅 π‘½πŸ‘ 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`

0.83𝑉1−0.5𝑉2−0.33𝑉3=0.66 …..(1)

Applying KCL at node 2

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

−0.2𝑉1+0.596𝑉2−0.066𝑉3=−0.33 …….(2)
Applying KCL at node 3

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

−𝑉1−𝑉2+2.5𝑉3=5 ………(3)
From (1), (2) and (3) we get,
𝑉1=2.46𝑉       π‘‰2=0.63𝑉       π‘‰3=3.23𝑉
Applying KCL,

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

`I` = −1.54π΄π‘š 𝐈(𝟎.πŸ“Ω)= 𝟏.πŸ“πŸ’π€π¦(←)

Concept: Three Phase Voltage Genration
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