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Node to Datum Circuit (EE)

  1. Mar 28, 2008 #1
    1. The problem statement, all variables and given/known data
    For the following circuit, use node-to-datum analysis to find the nodal voltages V1, V2, V3.
    http://img166.imageshack.us/img166/6205/ntd21qb1.th.gif [Broken]

    [tex]
    {\mathop{\rm V}\nolimits} _S = 9V,\;R_A = 3W,\;R_B = 4W,\;R_C = 6W,\;I_S = 3 A
    [/tex]


    2. The attempt at a solution

    [tex]
    \begin{array}{l}
    Node\;\;V_1 \;\; \Rightarrow \;\;V_1 = 4V \\
    \\
    Node\;\;V_2 \;\; \Rightarrow \;\frac{{V_2 - 4}}{3} + \frac{{V_2 }}{7} + \frac{{V_2 - V_3 }}{3} = 0 \\
    \\
    Node\;\;V_3 \;\; \Rightarrow \;\frac{{V_3 - V_2 }}{3} + 3 = 0 \\
    \\
    7\left( {V_2 - 4} \right) + 3V_2 + 7\left( {V_2 - V_3 } \right) = 0 \\
    7V_2 - 28 + 3V_2 + 7V_2 - 7V_3 = 0 \\
    17V_2 - 28 - 7V_3 = 0 \\
    17V_2 - 28 - 7\left[ {V_2 - 9} \right] = 0 \\
    17V_2 - 28 - 7V_2 + 63 = 0 \\
    10V_2 = - 35 \\
    \Rightarrow \underline {V_2 = - 3.5V} \;\; \\
    V_3 = - 3.5 - 9 = \underline { - 12.5V} \\
    \end{array}
    [/tex]

    Can someone please check my working?
    Thanks.
     
    Last edited by a moderator: May 3, 2017
  2. jcsd
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