Understanding Nodal Analysis: How Voltage at Node D is Calculated

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Nyasha
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Guys l would like to know how does the the voltage at node D become :

Vd=-(Vc-Va)=Va-Vc
 
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  • Handwritten circuit schematic with nodes labelled VA, VB, VC, VD and VE, a 5 V voltage source inside a dashed supernode, dependent sources 3VX and 2(VC - VA), resistors of 1 Ω, 2 Ω and 6 Ω, and current IX marked.
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Calculate ix = (VC-VA)/2. You see why this is, I hope. Ask if you don't.

Then the dependent source feeding VD has a voltage VD =-2*ix. Substituting what we calculated for ix above, we have VD = -2*ix = -2*(VC-VA)/2 = VA-VC.