QiLing Tools

💡DC Circuit Simulator - Build Circuits, Solve Node Voltages & Currents (Kirchhoff)

Build circuits on a grid the way you would on a lab bench. Pick a battery, resistor, bulb, switch, ammeter or voltmeter, tap a grid point to place it, and drag between grid points with the wire tool to connect things up. Select a part to change its EMF, internal resistance, resistance or bulb rating (engineering notation like 4.7k or 100m works), rotate it, swap its ends or delete it, and tap a switch to flip it. After every change the circuit is re-solved with modified nodal analysis (MNA): wires, ammeters and closed switches merge the grid points they join into one node, each node gets a KCL equation, each ideal battery adds a voltage constraint, and Gaussian elimination gives every node potential and battery current — the equations themselves are listed below the circuit. Node potentials are labelled on the canvas, yellow dots flow along the wires at a speed that reflects the current, bulbs glow according to their actual power versus rating, and meters show their readings; a table lists the current, voltage and power of every part and checks that power supplied equals power dissipated. Short-circuited or conflicting ideal batteries, open circuits and floating parts produce a clear message instead of an error. Examples include series, parallel, a voltage divider, a Wheatstone bridge, a two-loop Kirchhoff problem and a battery with internal resistance, and the circuit is saved in the page URL so you can share it with a link.

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How to use DC Circuit Builder & Solver

  1. 1Pick an example circuit, or start from the blank canvas
  2. 2Choose a part and tap a grid point to place it; use the wire tool to drag between grid points
  3. 3Use select/move to drag parts and flip switches; select a part to edit its values, rotate or delete it
  4. 4Watch the current animation, node potentials and meter readings, and read the parts table and MNA equations
  5. 5Copy the share link to send your circuit to someone else

FAQ

How does the tool solve the circuit?
It uses modified nodal analysis, the method behind SPICE-style simulators. Grid points joined by wires, ammeters and closed switches are merged into one node, and a battery’s negative terminal is taken as the 0 V reference. Every other node gets a Kirchhoff current-law equation — the currents leaving it sum to zero, with (φa − φb)/R for each resistor — and every ideal battery adds “positive terminal minus negative terminal = ε”. The linear system is solved by Gaussian elimination with partial pivoting, giving all node potentials and battery currents, from which each part’s current and power follow. The equations and solution are printed below the circuit.
Why does internal resistance lower the terminal voltage?
A real battery behaves like an EMF ε in series with an internal resistance r. With a current I flowing, Ir is dropped inside the battery, so the terminal voltage is U = ε − Ir and it sags more as the current grows. With an external resistance R, I = ε/(R + r). With the circuit open, I = 0 and a voltmeter across the terminals reads the full EMF; with a short circuit the current is at its maximum ε/r and the terminal voltage is zero. The internal-resistance example lets you open the switch or change R and watch both meters.
When is a Wheatstone bridge balanced?
The bridge has two parallel branches, R₁–R₂ and R₃–R₄, with a sensitive galvanometer joining their midpoints. When R₁/R₂ = R₃/R₄ the two midpoints sit at the same potential, no current flows through the galvanometer and the bridge is balanced — so knowing three resistors gives you the fourth. In the example R₄ is deliberately 310 Ω and a small current flows; change it to 300 Ω and the galvanometer reads zero.
What happens if I connect a meter the wrong way?
Meters here are ideal: a voltmeter has infinite resistance and an ammeter zero. Put a voltmeter in series and almost no current flows round the loop, so it reads close to the battery’s EMF. Put an ammeter across a component and it acts as a wire that shorts that component out, so the component carries no current and the ammeter may read a large value. Connect an ammeter straight across an ideal battery and you have a short circuit; the tool will warn that the current would be infinite.