Place parts on the board and watch current flow, bulbs light up and meters take readings as you build. Then solve circuit puzzles, from a single bulb to a staircase light with two switches.
Choose a part, then tap a grid line to place it. Drag with the wire tool to draw several wires at once. Tap a switch to flip it, and use Select to read any part's voltage, current and power. Load an example to compare series and parallel.
Examples:
Battery voltage
Current from battery
Total resistance
Total power
Keyboard: arrow keys move the cursor along the grid, Space turns it sideways, Enter uses the chosen part, Delete removes. Bulbs are rated 6 V 3 W (12 Ω). Wires, switches and ammeters count as almost zero resistance and voltmeters as almost infinite.
Pick a part from your tray and tap a grid line to place it; drag with Wire to draw several segments at once. Tap a placed switch to flip it, tap a placed part again to take it back, or use Eraser. Parts on a grey pad are fixed. Fewer parts and no hint earn three stars.
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What makes a circuit
An electric circuit is a closed loop that current can travel around. The battery does not create charge; it pushes the charge that is already in the wires, the way a pump pushes water around a closed pipe. Current leaves the + terminal, passes through the bulbs and resistors, and returns to the − terminal. If the loop is broken anywhere, by a cut wire, a removed bulb or an open switch, the push has nowhere to go and the current stops everywhere at once.
The direction from + to − is called conventional current, and every textbook diagram uses it. The particles that actually move in a metal wire are electrons, which carry negative charge and drift the opposite way, from − to +. Both descriptions give the same answers for every circuit on this page; the moving dots on the board follow the conventional direction.
Voltage, current and resistance
Three quantities describe every circuit. Voltage (V, measured in volts) is the push the battery gives each bit of charge. Current (I, in amperes) is how much charge passes a point each second. Resistance (R, in ohms, Ω) is how strongly a part opposes the flow. In the water picture, voltage is the pressure, current is the flow rate and resistance is a narrow section of pipe.
Ohm's law ties them together: V = I × R. A bulb on this page has a resistance of 12 Ω, so on a 6 V battery it carries I = 6 ÷ 12 = 0.5 A. Rearranged, the same law gives R = V ÷ I, which is how level 8 of the puzzle works: to get 0.5 A from 6 V you need 12 Ω in total, whether that is one resistor or several.
Series circuits: one path
In a series circuit the parts sit one after another on a single path, so the same current flows through every one of them. The resistances add up: two 12 Ω bulbs make 24 Ω, the current falls to 6 ÷ 24 = 0.25 A, and the battery's 6 V is shared, 3 V across each bulb. Load the Series example in the builder and tap each bulb to see those numbers.
Two things follow. Each bulb now gets half the voltage and half the current, so a quarter of the power, and glows much more dimly. And if one bulb fails, the single path is broken and every bulb goes out, which is why old strings of decorative lights went dark all at once. Level 7 turns this around on purpose: a switch placed across one bulb gives the current a shortcut past it.
Parallel circuits: many paths
In a parallel circuit each part has its own branch connected straight across the battery. Every branch gets the full battery voltage, so two 12 Ω bulbs in parallel each carry 0.5 A and shine exactly as brightly as one bulb alone. The battery supplies the sum of the branch currents, 1 A here. Add a third bulb and the battery has to deliver 1.5 A.
Because each branch is an extra path, the combined resistance is smaller than any single branch: 1/R = 1/R₁ + 1/R₂, so 12 Ω and 12 Ω in parallel act like 6 Ω. Houses are wired this way, so every lamp and socket gets the same voltage and can be switched on its own. Levels 4 to 6 practise it, ending with two switches that each control one bulb.
Mixed circuits and combining resistors
Real circuits mix both arrangements. The trick is to simplify step by step: replace each group that is purely series or purely parallel with a single equivalent resistor, then repeat. Three 4 Ω resistors in level 9 show it: two in parallel become 2 Ω, and that pair in series with the third gives 4 + 2 = 6 Ω, so 6 V drives exactly 1 A.
Series resistors also split the voltage in proportion to their size, an arrangement called a voltage divider. With 4 Ω and 12 Ω in series on 24 V, the current is 24 ÷ 16 = 1.5 A, so the 12 Ω resistor gets 1.5 × 12 = 18 V and the 4 Ω resistor the remaining 6 V. The Mixed example in the builder puts a voltmeter across a resistor so you can watch this happen.
Power and brightness
How bright a bulb glows depends on its power, the energy it turns into light and heat each second. Power is P = V × I, measured in watts, and with Ohm's law it can also be written P = I² × R or P = V² ÷ R. The bulbs here are rated 6 V 3 W: on 6 V they draw 0.5 A and use 3 W, which the simulator shows as 100% brightness.
Because power grows with the square of the voltage, halving the voltage cuts the power to a quarter. That is why two bulbs in series each show 25%, and why level 10 asks for a 12 Ω series resistance to dim a bulb to a quarter. Go the other way, 12 V on a 6 V bulb, and the power is four times the rating; the builder warns that the bulb would burn out.
Meters, switches and short circuits
An ammeter measures the current through itself, so it goes in series, in line with the part, and has almost no resistance. A voltmeter compares two points, so it goes in parallel, across the part, and has an enormous resistance so it barely disturbs the circuit. Put them the wrong way round and the results are dramatic: an ammeter across a bulb shorts it out, and a voltmeter in series blocks nearly all the current. Level 11 checks both.
A short circuit is a path with almost no resistance from one battery terminal back to the other. Ohm's law then predicts a huge current that heats the wire and drains or damages the battery; at home it is what fuses and circuit breakers are there to stop. The builder flags a short in red. Switches, finally, are just controllable gaps, and the staircase light in level 12 uses two two-way switches so that either one can always change the lamp.
How the simulator calculates
Each grid point is a node and each part joins two nodes. The simulator writes Kirchhoff's current law for every node (the current flowing in equals the current flowing out) and solves the resulting set of equations, a method called nodal analysis, every time you change something. Wires, closed switches and ammeters are given a tiny resistance of 0.0001 Ω, the battery 0.001 Ω of internal resistance and voltmeters 10 MΩ, which keeps the maths stable while matching ideal textbook values to well under 0.1%.
It is a model for learning, not an engineering tool. Bulbs are treated as fixed 12 Ω resistors, while a real filament's resistance rises several times as it heats up. Batteries never run down, wires never melt, and there are no capacitors, coils or alternating current. Within those limits, every number you see follows exactly from Ohm's law and the series and parallel rules described above.
Why are bulbs in series dimmer than bulbs in parallel?
In series the bulbs share the battery's voltage and the same, smaller current flows through both. Two identical bulbs each get half the voltage and half the current, so a quarter of the power. In parallel each bulb is connected straight across the battery and gets the full voltage, so it shines as if it were alone.
If parallel branches lower the total resistance, why don't the bulbs get brighter?
The lower total resistance means the battery supplies more current overall, but that extra current is shared out among the new branches. Each bulb still has the same voltage across it, so it carries the same current and glows the same. Only the battery works harder, which is why real batteries run down faster with many loads.
What exactly happens in a short circuit?
A wire with almost no resistance connects the battery's terminals, bypassing the bulbs. By Ohm's law the current becomes enormous, limited only by the battery's internal resistance. The bulbs go dark because the current takes the easy path, the wire heats up and the battery drains quickly or is damaged. Fuses and circuit breakers exist to cut this off.
How do I connect an ammeter and a voltmeter correctly?
The ammeter goes in series: break the circuit and put it in the gap so the current you want to measure passes through it. The voltmeter goes in parallel: connect its two ends to the two ends of the part you are measuring, without breaking anything. Puzzle level 11 asks you to do both at once.
How does a staircase light with two switches work?
Each switch is a two-way switch that connects its common wire to one of two paths, a or b. The two switches are joined by both paths, so the lamp lights only when both pick the same path. Flipping either switch makes the paths disagree, or agree again, so the lamp always changes. In the US these are called 3-way switches.
How accurate is the simulator?
It solves the circuit exactly by nodal analysis, using tiny resistances for wires and a very large one for voltmeters, so its numbers match the ideal textbook answers to well under 0.1%. The simplifications are in the parts: bulbs keep a fixed 12 Ω instead of changing with temperature, batteries never run down, and there are no capacitors, coils or alternating current.