Determine the values of the node voltages va and vb for the circuit shown in the figure. The first node equation:
the voltage source voltage is related to the node voltages by vb- va = 12 => vb = va + 12. To write the second node equation, we must decide what to do about the voltage source current. KCL can be applied to the problem to generate the 2nd node equation : va/6 + vb/3 = -2. In summary, the node equations are vb – va = 12 and va/6 + vb/3 = -2. Solving the node equations gives va = 12 V; and vb = 0V
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