How to formulate equations using node voltage method

Node voltage method equation method uses Kirchhoff's current law (KCL): select the reference node to be 0 voltage. Assign unknown voltage variables to non-reference nodes. Applying KCL equalizes the current flowing into and out of each non-reference node. Simplify equations, use Ohm's law, etc. Solve the system of equations to obtain the non-reference node voltage value.

Node voltage method equation

Clear answer to the question:

The node voltage method equation requires the use of Kirchhoff's current law (KCL).

Detailed answer:

Kirchhoff's current law (KCL):
In any closed circuit, flow into any node The sum of the currents is equal to the sum of the currents flowing out of that node.

Node voltage method:

1. Select a reference node: Select a node as the reference node, and its voltage is defined as 0.
2. Assign unknown voltages to non-base nodes: Assign an unknown voltage variable to each non-base node.
3. Applying KCL: For each non-base node, write the equation for the current flowing into and out of that node.
4. Simplify the equation: Use information such as Ohm's law and a known voltage source to simplify the current equation into an equation containing only the unknown voltage variable.
5. Solving a system of equations: Use the matrix method or other methods to solve a system of equations consisting of unknown voltage variables.

Equation example:

Consider the following circuit:

[Circuit diagram]

Select node A as the base node, Nodes B and C are non-base nodes. The current flowing into node B is:

<code>iB = (VB - VA) / R1</code>

The current flowing out of node B is:

<code>iB = (VB - VC) / R2</code>

According to KCL, the current flowing into and out of node B is equal:

<code>(VB - VA) / R1 = (VB - VC) / R2</code>

Similarly, For node C:

<code>(VC - VB) / R2 = (VC - 0) / R3</code>

Simplify and solve these equations to get the values ​​of VB and VC.

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