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What is Nodal analysis?

A method that takes the voltage of each node (its potential relative to a reference node) as the unknowns, applies Kirchhoff's current law at each node and solves the resulting simultaneous equations. There are "number of nodes − 1" unknowns, so it needs few equations for circuits with current sources or many parallel branches. Circuit simulators such as SPICE use modified nodal analysis, an extension that also handles voltage sources.

Japanese name: 節点解析

Nodal analysis appears in 2 practice questions across 2 topics, including Circuit Analysis: AC, Linear Circuits and Transients, Analog and electronic circuits.

Field: Circuit Analysis: AC, Linear Circuits and Transients

Try it: questions about Nodal analysis

In the circuit in the figure, E = 12 V, R1 = 4 Ω and J = 2 A. R2 is removed. Which of the following is the Thevenin equivalent circuit (equivalent voltage Vth and equivalent resistance Rth) seen from the two terminals to which R2 was connected (node A and ground)?

  1. AVth = 12 V, Rth = 4 Ω
  2. BVth = 20 V, Rth = 4 Ω
  3. CVth = 20 V, Rth = 3 Ω
Show answer and explanation

Answer: B. Vth = 20 V, Rth = 4 Ω

Vth is the voltage with the terminals open; all 2 A of J then flows through R1 toward the positive terminal of E, so Vth = E + J R1 = 12 + 2 × 4 = 20 V. Rth is the resistance seen from the terminals with the voltage source shorted and the current source opened, which is just R1 = 4 Ω. Connecting R2 = 12 Ω to this equivalent gives VA = 20 × 12/(4 + 12) = 15 V, matching the result of nodal analysis. As a Norton equivalent, it is a current source equal to the current with the terminals shorted, E/R1 + J = 5 A, in parallel with 4 Ω.

Which correctly states Kirchhoff's current law (first law)?

  1. AThe sum of currents flowing into a node equals the sum of currents flowing out
  2. BThe sum of voltages around a closed loop is zero
  3. CThe current through a resistor is proportional to the voltage
Show answer and explanation

Answer: A. The sum of currents flowing into a node equals the sum of currents flowing out

Kirchhoff's current law states that the currents flowing into a node equal those flowing out, expressing conservation of charge. Combined with the voltage law (voltages around any closed loop sum to zero), it lets you solve for every current and voltage in a complex circuit with simultaneous equations. Circuit simulators such as SPICE apply this law at every node in nodal analysis.

Nodal analysis in the explanations

Questions that mention Nodal analysis (2)

  1. In the circuit in the figure, E = 12 V, R1 = 4 Ω and J = 2 A. R2 is removed. Which of the following is the Thevenin equivalent circuit (equivalent voltage Vth and equivalent resistance Rth) seen from the two terminals to which R2 was connected (node A and ground)?
  2. Which correctly states Kirchhoff's current law (first law)?

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Related terms

Thevenin's theorem Norton's theorem SPICE Admittance Impedance Mesh analysis Partial fraction decomposition Phasor Q factor (quality factor) Reactance

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