🔌

Nodal Analysis Overview

Aug 24, 2025

Overview

This lesson covers nodal analysis, a method based on Kirchhoff's Current Law (KCL), for finding unknown voltages and sometimes currents in electrical circuits using systematic node equations.

Introduction to Nodal Analysis

  • Nodal analysis primarily uses KCL to determine unknown voltages at nodes in a circuit.
  • While it typically solves for voltages, it can be adapted to find currents as well.
  • Ground (reference node) is chosen for convenience, usually the node most commonly at 0 volts.

Example 1: Solving for an Unknown Voltage

  • Label all nodes; assign ground to one node (often the negative terminal).
  • Use KCL: sum of currents leaving a node equals currents entering (ΣI_out = ΣI_in).
  • Express each current using Ohm’s Law: I = (V_nodeA - V_nodeB) / R.
  • Write the KCL equation for the key node, substitute Ohm's Law for each branch.
  • Combine into a single equation and solve for the unknown node voltage.
  • Example calculation: node B voltage (VB) is found to be 40 V, which is the desired VX.

Example 2: Identifying Voltages in Parallel Components

  • Components in parallel share the same voltage drop.
  • Directly identify voltages across parallel components without further calculation (e.g., V2 = 20 V).
  • To find another voltage (V1), label all nodes and set the bottom node as ground.
  • Apply KCL at the node of interest, substitute using Ohm’s Law as before.
  • Solve for the unknown node voltage (VA = 16 V, so V1 = 16 V).

Finding Power Dissipation

  • To find resistor power: use (P = V^2/R), where V is the voltage across the resistor.
  • The sign of the voltage does not matter due to squaring (always yields positive power).

Key Terms & Definitions

  • Nodal Analysis — A technique applying KCL to find unknown voltages in a circuit.
  • Kirchhoff’s Current Law (KCL) — The sum of currents entering a node equals the sum leaving it.
  • Ground (Reference Node) — A node assigned 0 V to serve as a voltage reference for the circuit.
  • Ohm’s Law — Relates current, voltage, and resistance: (I = (V_A - V_B)/R).
  • Parallel Components — Circuit elements connected across the same two nodes, thus sharing voltage.

Action Items / Next Steps

  • Practice nodal analysis on homework problems, including finding node voltages and resistor power dissipation.
  • Review textbook sections on nodal analysis and KCL.

Full transcript