Circuit builder

Build your own circuit — add up to 15 resistors, bulbs and capacitors, switch between series and parallel, set the battery's voltage and internal resistance, and press Show current flow to watch charge actually move through the wires. Every number is computed exactly from the standard circuit-theory formulas — see exactly which one is driving the result in the Formula in use panel below the circuit.

Lessons

Pick your class, read the steps, then try them right in the builder below.

Class 10 — Ohm's law and resistors in series

Concept: Ohm's law says V = IR. Put resistors in series and the same current I flows through all of them, while the battery voltage splits across them: R_s = R₁ + R₂ + R₃ + …

Load the Series — R_s = R₁+R₂+R₃ preset above (10, 20, 30Ω at 12 V).
Read the Formula in use panel under the circuit — it shows R_s = 10 + 20 + 30 = 60Ω, then I = 12/60 = 0.2 A.
Now drag any resistor's Resistance slider on the right up or down and watch the current in the Total current stat change immediately — every resistor shares the exact same current, since it's one loop.

Takeaway: add up resistances directly in series; the total current depends on that sum, not on any single resistor alone.

Class 10 — Resistors in parallel

Concept: in parallel, every branch gets the full battery voltage, and 1/R_p = 1/R₁ + 1/R₂ + 1/R₃ … — the equivalent resistance is always smaller than the smallest individual resistor.

Load the Parallel — 1/R_p = 1/R₁+1/R₂+1/R₃ preset above.
Note the Equivalent R stat (5.0Ω) — smaller than any of the 10, 20, 20Ω resistors feeding it.
Tap a resistor's × to remove it, and watch the other branches' currents stay exactly the same — removing one branch doesn't disturb the others, unlike series.

Takeaway: this is why household wiring is parallel — one appliance failing or being unplugged doesn't cut power to the rest of the house.

Class 12 — Electric power: P = VI = I²R = V²/R

Concept: the same power dissipated by a resistor can be written three equivalent ways, and all three must always agree.

Load the Power — P = VI = I²R = V²/R preset above (a single 20Ω resistor at 10 V).
Check the Total power stat (5 W), then verify by hand: I = V/R = 0.5 A, so I²R = 0.25×20 = 5 W, and V²/R = 100/20 = 5 W — all three match.
Raise the Battery EMF slider and watch power rise — notice it grows with the square of the voltage, not in direct proportion.

Takeaway: doubling the voltage across a fixed resistor quadruples the power, because power depends on V².

Class 12 — Capacitors in a DC circuit

Concept: once a capacitor is fully charged in a DC circuit, no more current flows into it — at that point Q = CV.

Load the Capacitor — Q = CV preset above (a resistor and a 220µF capacitor in series at 9 V).
Read the Total current stat — it's 0 A, and the toolbar note explains why: the capacitor blocks the loop at steady state.
Check the capacitor's own row in the table: Q = 1980.0µC, exactly 220µF × 9 V.
Try raising the capacitance slider — the stored charge rises in direct proportion, since Q = CV with V fixed.

Takeaway: a capacitor charges up and then stops current cold — it behaves nothing like a resistor once steady state is reached.

Class 12 — Internal resistance and terminal voltage

Concept: a real cell isn't a perfect voltage source. Once current flows, its terminal voltage drops below its EMF: V = E − Ir.

Load the Internal resistance — V = E−Ir preset above (a 5Ω resistor, r = 1Ω, at 6 V).
Compare Battery EMF (6.0 V) against Terminal voltage (5.00 V) in the stats row — the gap is exactly I×r = 1×1 = 1 V.
Drag the Internal resistance (r) slider to 0 and watch the terminal voltage snap back up to equal the EMF exactly — a truly ideal cell.

Takeaway: the more current a real cell delivers, the further its terminal voltage sags below its rated EMF.

Load a ready-made circuit:

◫ Resistor

💡 Bulb

Capacitor

Tap a component above to arm it, then tap the dashed + slot to add it to the circuit (up to 15). Tap the × on any component to remove it.

Slot	Component	Value	Voltage	Current	Power / charge

Series vs parallel, in one sandbox

Series — one loop, one current. Every component carries the same current; the battery voltage splits across them in proportion to resistance (V = IR for each). Remove every component and the loop is open — nothing lights up, matching the real "one broken bulb kills the string" behaviour of old series fairy lights.

Parallel — every branch gets the full terminal voltage directly, and draws its own current independently (I = V/R). Removing a branch just means one fewer path; the others keep working exactly as before — the real reason household wiring is parallel, not series.

The capacitor is the odd one out: once a DC circuit reaches steady state a fully charged capacitor blocks current completely. In series, that stops current everywhere in the loop and the whole EMF appears across the capacitor (Q = CV). In parallel, only that branch goes to zero current — it just charges up to the terminal voltage while every other branch keeps flowing normally.

Internal resistance — a real cell isn't a perfect voltage source; it has some internal resistance r, so the voltage at its terminals drops below the EMF once current flows: V = E − Ir. Set r above zero and watch "Terminal voltage" fall away from "Battery EMF" as you add more components.

Exactly two idealisations, both disclosed: the bulb is a fixed 9Ω resistor (a real filament's resistance actually rises with temperature — modelling that needs a separate thermal simulation, not a shortcut in the circuit maths), and the wires plus the battery's EMF are ideal (no resistance of their own; every ohm you see comes from a component you placed or the internal-resistance slider). Every equation applied to whatever you build — Ohm's law, the series and parallel combination rules, Kirchhoff's laws, and the capacitor's DC steady-state behaviour — is solved exactly, with no fudge factors.

Part of Forces — see Learn for the class 10 & 12 electricity topics this maps to.

Formula sheet — current electricity

Every formula from the class 12 current-electricity unit, in one place. The ones marked live plug in the numbers from the circuit you've built above.

Test yourself

Pick Class 10 or Class 12 in the physics quiz to test yourself on current, resistance and circuits — 10 random questions, with an explanation for every answer.

Take the physics quiz →