Understanding Nodal Analysis: How Voltage at Node D is Calculated

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SUMMARY

The voltage at node D is calculated using the formula Vd = -(Vc - Va), which simplifies to Vd = Va - Vc. The current ix is determined by the equation ix = (Vc - Va) / 2. Additionally, the dependent source feeding node D has a voltage defined as VD = -2 * ix, leading to the final expression VD = VA - VC after substitution. This analysis clarifies the relationships between the voltages at nodes A, C, and D in the circuit.

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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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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.
 

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