How to use the Nodal Analysis Solver
- 1. Write KCL at each nodeCurrents leaving the node: (V1 − V2)/5 + V1/2 = 3.
- 2. Or enter [G | I]Rows like 0.7 −0.2 | 3.1.
- 3. SolveGet V1…V4, the working and the current in each shared branch.
Nodal analysis method
Pick a reference (ground) node and label the other node voltages V1, V2, … . At every non-reference node, the sum of currents leaving through resistors equals the source current entering. A resistor R between nodes i and j carries (Vi − Vj)/R. Collected together, the equations give [G][V] = [I]. The diagonal is the sum of conductances at each node, and the off-diagonal terms are minus the conductance between two nodes.
Worked example (Hayt): 3.1 A enters node 1 and 1.4 A enters node 2. A 2 Ω resistor goes from node 1 to ground, 5 Ω joins the two nodes, and 1 Ω goes from node 2 to ground. That gives 0.7V1 − 0.2V2 = 3.1 and −0.2V1 + 1.2V2 = 1.4. Δ = 0.84 − 0.04 = 0.8, Δ1 = 4, Δ2 = 1.6, so V1 = 5 V and V2 = 2 V.
Exam tips for nodal analysis
- Choose the node with the most connections as the reference, to save equations.
- A voltage source between a node and ground fixes that node voltage. A source between two nodes needs a supernode.
- Write every current as leaving the node, so all the resistor terms have the same sign.
- Nodal analysis is usually shorter than mesh analysis when the circuit has fewer nodes than meshes.
Fractions such as V1/2 and (V1 − 10)/4 can be typed directly.
Frequently asked questions
What units should I use?
Volts, amperes and siemens (or ohms inside the fractions). If you type conductances in mS and currents in mA, the answer is still in volts.
Can I include a voltage source in the KCL equations?
Yes, as a known value: a source of 10 V through 2 Ω to node 1 gives the term (V1 − 10)/2.
How do I find the current in a resistor afterwards?
The table lists the current between every pair of nodes joined by a conductance. For a resistor to ground, use Vi/R.
Is this tool free?
Yes. You fill in a short form once to see your result, and the other Uncodemy tools then open without it. All the maths runs in your browser.