Capacitor Network Analyzer

Physics Electricity and Magnetism • Electric Potential and Capacitance

Written by STEM Calculators Team Published January 12, 2026 Updated February 24, 2026

4. Capacitor Network Analyzer

Build a capacitor network by clicking on the schematic, then compute the equivalent capacitance $C_{eq}$ and the charge/voltage/energy distribution. Mixed series/parallel networks are supported using nodal analysis.

Inputs support: pi, e, sqrt(), sin, cos, exp, log. Use * for multiplication.

Setup

Given: $V_{AB}$ (V): $Q_A$ (C): Capacitor unit for entry: Snap to grid: Grid:

How to build: choose a tool below, then click on the schematic. Use the mouse wheel (or trackpad) to zoom; drag empty space to pan; double-click to reset view.

Tool: Select/Move

Ready

Schematic editor (A → B)

Click to build • pan/zoom • select to edit values

Hover: …

Selection

Click a node or capacitor to edit it.

Capacitors

Name	Between	Value

Tip: in Add capacitor tool, click node 1 then node 2. Select the capacitor to set its value.

Steps

Build a network and click Solve.

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Theory

What this tool computes

A capacitor network is a set of capacitors connected between two terminals (here labeled A and B). The tool computes the equivalent capacitance $C_{eq}$ seen between A and B, and (optionally) the distribution of voltages, charges, and energies on each capacitor.

Equivalent capacitance

By definition: \[ C_{eq} = \frac{Q_A}{V_{AB}}, \] where $V_{AB}=V_A - V_B$ is the applied terminal voltage and $Q_A$ is the total charge leaving terminal A into the network.

Series/parallel reduction works only for simple layouts. This tool supports mixed networks (and many non-reducible ones) using nodal analysis.

Nodal analysis (works for mixed networks)

The tool applies a test voltage $V_A=1$, $V_B=0$ and solves the unknown potentials of all internal nodes. At each internal node $i$, charge balance gives: \[ \sum_{j} C_{ij}\,(V_i - V_j)=0. \]

After the node voltages are found, the charge at terminal A is: \[ Q_A = \sum_{j} C_{Aj}\,(V_A - V_j). \] Because $V_{AB}=1$ in the test problem, the result is: \[ C_{eq}=Q_A. \]

Scaling to your input

If you enter a terminal voltage $V_{AB}$, then total charge is: \[ Q_A=C_{eq}\,V_{AB}. \] If you enter total charge $Q_A$, then: \[ V_{AB}=\frac{Q_A}{C_{eq}}. \] All node voltages scale linearly with $V_{AB}$.

Per-capacitor charge and energy

For any capacitor between nodes $i$ and $j$: \[ \Delta V = V_i - V_j,\qquad Q = C\,\Delta V. \]

Energy stored: \[ U=\frac12\,C\,(\Delta V)^2. \]

How to build a circuit in the editor

Add node: click to place junction points.
Add capacitor: click node 1 then node 2 to connect them.
Select/Move: click a node/capacitor to edit; drag nodes to rearrange.
Delete: click an element to remove it.
Pan by dragging empty space; zoom with wheel/trackpad; double-click resets view.

Tip: Use the presets to instantly create series, parallel, or a mixed example.

Schematic editor (A → B)

Steps

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