⚡ DC Circuit Builder

Kirchhoff’s Current Law states that the total current entering a junction equals the total current leaving it. No charge is created or destroyed at a junction — what flows in must flow out.

When enabled, click any junction (where two or more components meet) to see all the currents flowing in and out, displayed in a draggable equation box.

1. Build a circuit with at least one junction (e.g. a parallel circuit) and ensure it is simulating.
2. Tick the KCL (1st Law) checkbox.
3. Click on any junction (node dot) in the circuit.
4. An equation box appears showing currents entering (positive) and leaving (negative) that junction, with the sum equalling zero.
5. Drag the equation box to reposition it.
6. Click a different junction to update, or untick to clear.

• The circuit must be simulating (connected with a battery/source).
• Not available when a rheostat is in the circuit (use variable resistors instead).
• Click on junction points — these are the dots where wires and components connect.

Kirchhoff’s Voltage Law states that for any closed loop in a circuit, the sum of the EMFs equals the sum of the voltage drops across the components. Equivalently, the algebraic sum of all voltages around any closed loop is zero.

When enabled, you click on the highlighted nodes (junction dots) sequentially to trace a closed loop in the direction you choose. An equation box then displays the EMFs and voltage drops around that loop.

1. Build and simulate a circuit.
2. Tick the KVL (2nd Law) checkbox. The circuit’s nodes are highlighted.
3. Click the first node to begin your loop.
4. Click adjacent nodes one at a time to extend the path. Each step adds the component between the two nodes. The direction you trace determines the sign convention.
5. When you have 3 or more nodes, click back on the starting node to close the loop.
6. The equation box appears showing each EMF and voltage drop around the loop, summing to 0 V.
7. Drag the equation box to reposition it.
8. Click the last node to undo the previous step. Untick to clear everything.

• The circuit must be simulating (connected with a battery/source).
• Not available when a rheostat is in the circuit (use variable resistors instead).
• You must click on the highlighted node dots — not on the components themselves. Each click must be a node that is directly adjacent (connected by one component) to the previous node.

An I-V characteristic plots current (I) against voltage (V) for a component, revealing whether it obeys Ohm’s Law. A straight line through the origin means the component is ohmic (constant resistance). A curve means the resistance changes — for example, a filament bulb curves because its resistance increases as it heats up.

The graph is built by sweeping the variable resistor from minimum to maximum while recording the ammeter and voltmeter readings at each position.

You need all three of these in your circuit:
• A variable resistor or rheostat — this is swept to vary the current.
• An ammeter — measures the current through the test component.
• A voltmeter — measures the voltage across the test component.

The voltmeter’s probes define which component is being characterised — place them across the component you want to test (e.g. a bulb, resistor, or LED).

1. Build the circuit with a battery, variable resistor, ammeter, and voltmeter.
2. Connect the voltmeter probes across the component you want to characterise.
3. Tick the I-V Graph checkbox.
4. The graph appears, plotting I vs V as the variable resistor sweeps automatically.
5. Drag the graph title bar to reposition it.
6. Click the graph to enlarge it full-size; click outside to shrink back.
7. Click individual data points to see the exact V and I readings.
8. Use the 1 Quadrant / 4 Quadrant radio buttons to change the axis range (4 Quadrant shows negative values too).

• For a filament bulb, set the variable resistor’s range comparable to the bulb’s resistance (e.g. 0–30 Ω) for a smooth curve. A very high range (e.g. 0–10 kΩ) concentrates most data points near zero.
• For an LED, the graph shows the characteristic “knee” — no current below the forward voltage, then rapid increase.
• For a fixed resistor, you should see a straight line (Ohm’s Law).

A V-I terminal characteristic plots the battery’s terminal voltage (V) against the current (I) it delivers. For a real battery with internal resistance r, the terminal voltage decreases as current increases, following:

V = ε − Ir

where ε is the EMF (no-load voltage). This produces a straight line with a negative slope equal to −r. The y-intercept gives the EMF and the x-intercept gives the short-circuit current.

You need all of these:
• A battery with internal resistance — select the battery, then set r > 0 in the properties panel and tick “Show internal resistance”.
• A variable resistor or rheostat — swept to vary the load.
• An ammeter — measures the circuit current.
• A voltmeter — placed across the battery terminals to measure terminal voltage.

1. Build the circuit with a battery (set internal resistance r > 0), variable resistor, ammeter, and voltmeter across the battery.
2. Tick the V-I Graph checkbox.
3. The graph plots terminal voltage vs current as the variable resistor sweeps.
4. Drag the title bar to reposition. Click to enlarge.
5. Click data points for exact readings.
6. The graph displays the calculated EMF (ε) and internal resistance (r) from the line of best fit.

• Steep line = high internal resistance (battery voltage drops quickly under load).
• Shallow line = low internal resistance (voltage stays more constant).
• Where the line crosses the y-axis = EMF (voltage with no current flowing).
• Where the line crosses the x-axis = short-circuit current (ε/r).

1. Click Save Circuit to generate a text code representing your entire circuit.
2. The code contains all components, positions, connections, settings, and display options.
3. Click Copy to Clipboard to copy the code.
4. Paste the code anywhere you like — a document, email, message, or note — to keep it for later.

1. Click Load Circuit.
2. Paste a previously saved circuit code into the text box.
3. Click Load Circuit to restore it.
4. This replaces whatever is currently on the canvas with the saved circuit, including all display settings and graph states.

• Codes start with DCCB1: — this identifies them as DC Circuit Builder saves.
• You can share codes with other people — they just paste it into their Load dialog.
• Save codes capture everything: component values, wiper positions, switch states, label positions, heat/light source positions, revealed labels, graph states, and all display toggles.
• Use Ctrl+Enter as a shortcut to load, or Escape to cancel.