In the node-voltage method, at which points are equations formed and which law is applied?

In the node-voltage method, at which points are equations formed and which law is applied?

• A. At the reference node using KCL.
• B. At each non-reference node using KVL.
• C. At each non-reference node using KCL.
• D. At each branch using Ohm's law alone.

Answer: (C)

The main idea is that the node-voltage method writes equations by enforcing current balance at each non-reference (non-ground) node using Kirchhoff's current law. You choose a reference node and set its voltage to zero. At every other node, you sum the currents flowing into or out of that node and set the sum to zero. Currents through connected elements are expressed in terms of node voltages (for resistors, using Ohm’s law: current = (voltage difference)/R; for current sources, the known value is included directly). Solve the resulting linear equations for the unknown node voltages relative to the reference. This is why the approach is not formed at the reference node (its voltage is defined as zero) and not done with Kirchhoff’s voltage law in this method (KVL is the basis of loop/m mesh analysis, not the node-voltage method). It also isn’t built by writing equations for each branch using Ohm’s law alone; you need the overall node current balance that ties all connected branches together at each node.

The main idea is that the node-voltage method writes equations by enforcing current balance at each non-reference (non-ground) node using Kirchhoff's current law. You choose a reference node and set its voltage to zero. At every other node, you sum the currents flowing into or out of that node and set the sum to zero. Currents through connected elements are expressed in terms of node voltages (for resistors, using Ohm’s law: current = (voltage difference)/R; for current sources, the known value is included directly). Solve the resulting linear equations for the unknown node voltages relative to the reference.

This is why the approach is not formed at the reference node (its voltage is defined as zero) and not done with Kirchhoff’s voltage law in this method (KVL is the basis of loop/m mesh analysis, not the node-voltage method). It also isn’t built by writing equations for each branch using Ohm’s law alone; you need the overall node current balance that ties all connected branches together at each node.