# Node to Datum Circuit (EE)

• Engineering
1. Homework Statement
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]

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

2. The attempt at a solution

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

Can someone please check my working?
Thanks.

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