Forces / Circuit builder

Electricity

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. The tabs after Series and Parallel switch the same playground to Kirchhoff's laws, RC charging, the bridges, the potentiometer, meters, cells and electron drift.

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.

Class 12 — Kirchhoff's laws

Concept: some circuits cannot be reduced by the series and parallel rules. Two laws always work: at a junction the currents in equal the currents out, and round any closed loop the potential changes add up to zero.

In Circuit experiments open Kirchhoff's laws: E₁ = 12 V, E₂ = 6 V, R₁ = 2 Ω, R₂ = 4 Ω, R₃ = 6 Ω.
The junction rule gives I₃ = I₁ + I₂; the loop rule on each side gives 12 − 2I₁ − 6I₃ = 0 and 6 − 4I₂ − 6I₃ = 0.
Solving: V_A = 8.182 V, I₁ = 1.909 A, I₂ = −0.545 A and I₃ = 1.364 A.
The minus sign means I₂ really flows the other way: cell 2 is being charged by cell 1. Check the energy: the cells supply 22.909 − 3.273 = 19.636 W, and the resistors turn exactly 19.636 W into heat.
Set E₂ to 0: cell 2 is now just a wire, and I₁ = 2.727 A, I₂ = −1.636 A, I₃ = 1.091 A.

Takeaway: ΣI = 0 at a junction (charge), Σ(E − IR) = 0 round a loop (energy); a negative answer only means the current runs against the arrow you guessed.

Class 12 — Charging and discharging a capacitor

Concept: through a resistor a capacitor charges gradually, with time constant τ = RC.

Open Charging a capacitor (RC) with E = 12 V, R = 10 kΩ and C = 100 µF: τ = 10 000 × 0.0001 = 1 s, and the first current is 12 ÷ 10 000 = 1.2 mA.
After one τ the voltage has reached 63.2% of 12 V = 7.58 V and the current has fallen to 36.8% (0.44 mA). After 5τ (5 s) it is 99.3% charged.
Choose Only discharge: the voltage falls as 12e^−t/RC, to 37% (4.42 V) after 1 s.
Double C to 200 µF: τ becomes 2 s, so charging takes twice as long, and the final charge CE doubles to 2.4 mC.
The energy graph: the capacitor ends with ½CE² = 7.2 mJ, and another 7.2 mJ has been turned into heat in R, so half the cell's energy is wasted whatever R is.

Takeaway: V_C = E(1 − e^−t/RC) when charging, E e^−t/RC when discharging; τ = RC.

Class 12 — Wheatstone bridge and meter bridge

Concept: a bridge is balanced when no current flows through the galvanometer, which happens when P ÷ Q = R ÷ S.

Open Wheatstone & meter bridge with P = 100 Ω, Q = 200 Ω and the unknown S = 30 Ω. At R = 60 Ω the bridge is not balanced and about 10.7 mA flows through G.
Slide R down to 15 Ω: the needle comes to zero. P ÷ Q = 0.5 and R ÷ S = 15 ÷ 30 = 0.5, so S = QR ÷ P = 200 × 15 ÷ 100 = 30 Ω.
The graph of galvanometer current against R crosses zero at the balance value and changes sign: that is how a null method works.
Switch to the meter bridge with R = 20 Ω and S = 10 Ω. The balance point is at l = 100R ÷ (R + S) = 66.67 cm; at l = 66.7 cm the galvanometer reads zero and S = 20 × 33.3 ÷ 66.7 = 10 Ω.
At l = 66 cm you would read S = 10.30 Ω: a 0.67 cm error makes a 3% error in S, which is why the balance point should be near the middle of the wire.

Takeaway: S = QR ÷ P; in the meter bridge S = R(100 − l) ÷ l.

Class 12 — The potentiometer

Concept: a potentiometer compares potential differences without drawing current from the cell at balance.

Open Potentiometer. A driver cell of 4 V with a 10 Ω rheostat sends 0.2 A through the 10 m wire (10 Ω), so the potential gradient is k = 2 V ÷ 10 m = 0.2 V/m.
Cell 1 (1.5 V) balances at l₁ = 1.5 ÷ 0.2 = 7.5 m; cell 2 (1.1 V) at l₂ = 5.5 m. E₁ ÷ E₂ = 7.5 ÷ 5.5 = 1.364.
Raise the rheostat to 40 Ω: k falls to 0.08 V/m and the balance length of cell 1 grows to 18.75 m, off the end of the wire, so there is no balance point. Use a larger driver EMF or a smaller rheostat.
Choose internal resistance (E = 1.5 V, r = 2 Ω, R = 10 Ω). Open circuit l₁ = 7.5 m; with R across the cell V = 1.25 V and l₂ = 6.25 m, so r = 10 × (7.5 − 6.25) ÷ 6.25 = 2 Ω.

Takeaway: E = kl, so E₁/E₂ = l₁/l₂, and r = R(l₁ − l₂)/l₂. A voltmeter reads the terminal voltage; a potentiometer measures the EMF.

Class 12 — Ammeter and voltmeter from a galvanometer

Concept: a small shunt in parallel makes an ammeter; a large resistance in series makes a voltmeter.

Open Ammeter & voltmeter with a galvanometer of 1 mA full scale and 50 Ω. For a 2 A ammeter S = 0.001 × 50 ÷ (2 − 0.001) = 0.02501 Ω, and the ammeter's resistance is 0.025 Ω.
Switch to voltmeter for 10 V: R = 10 ÷ 0.001 − 50 = 9950 Ω, so the voltmeter has 10 000 Ω (1000 Ω per volt).
Open Reading errors with R = 100 Ω, R_A = 2 Ω, R_V = 5000 Ω. With the voltmeter across R alone V ÷ I = 98.04 Ω (−1.96%); across R and the ammeter it is 102 Ω (+2%).

Takeaway: an ideal ammeter has zero resistance and an ideal voltmeter infinite resistance; use the first arrangement for low resistances and the second for high ones.

Class 12 — Cells in a battery and maximum power

Concept: combining cells changes the EMF and the internal resistance; a load takes the most power when its resistance equals the battery's internal resistance.

Open Cells & maximum power: 12 cells of 1.5 V and 0.5 Ω, joined 3 in series in each of 4 rows: E = 4.5 V and r = 3 × 0.5 ÷ 4 = 0.375 Ω.
With R = 2 Ω the current is 4.5 ÷ 2.375 = 1.895 A, the power 7.18 W and the efficiency 84.2%.
All 12 in series: E = 18 V, r = 6 Ω, I = 2.25 A. All in parallel: E = 1.5 V, r = 0.042 Ω, I = 0.735 A. For this 2 Ω load the best choice is 6 in series (r = 1.5 Ω): I = 2.57 A.
Slide R on the power graph: the power peaks at R = r = 0.375 Ω with P = E² ÷ 4r = 13.5 W, but the efficiency there is only 50%.

Takeaway: n in series, m rows: E = nE_cell, r = nr_cell/m; maximum power when R = r.

Class 10 & 12 — Resistivity and drift of electrons

Concept: R = ρL ÷ A: the resistance depends on the material, the length and the area, and metals get more resistive when heated.

Open Resistivity & drift with a copper wire 2 m long, 1 mm across, at 0.1 V: R = 1.68 × 10⁻⁸ × 2 ÷ 7.854 × 10⁻⁷ = 42.8 mΩ and I = 2.34 A.
Double the length: R doubles. Double the diameter: the area is four times as big, so R falls to a quarter.
Choose nichrome at 300 °C: ρ = 1.22 × 10⁻⁶ Ωm, R = 3.1 Ω and I = 32 mA, about 70 times less current than copper. Its resistivity hardly changes with temperature (α = 0.0004 per °C), which is why heaters use it.
Back to copper: the drift speed is only 0.22 mm/s, though the electrons move randomly at about 10⁶ m/s. The mean time between collisions is τ = m ÷ ne²ρ = 24.9 fs.

Takeaway: R = ρL/A; I = nAev_d; v_d = eEτ/m; ρ rises with temperature in metals.

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.

The physics behind it

Formulas used in this lab

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.

Formulas for the circuit experiments

Kirchhoff's laws Class 12

Junction rule: ΣI_in = ΣI_out (conservation of charge)
Loop rule: Σ(EMF) = Σ(IR) round a closed loop (conservation of energy)
Sign convention: a resistor crossed along the current: −IR; a cell crossed from − to +: +E
Two cells, three resistors: V_A = (E₁/R₁ + E₂/R₂) ÷ (1/R₁ + 1/R₂ + 1/R₃)

Charging and discharging a capacitor Class 12

Time constant: τ = RC
Charging: q = CE(1 − e^−t/RC); V_C = E(1 − e^−t/RC); I = (E/R)e^−t/RC
Discharging: q = q₀e^−t/RC; I = −(q₀/RC)e^−t/RC
After τ, 5τ: 63.2% and 99.3% charged; 36.8% and 0.7% left when discharging
Energy: stored ½CE²; the same amount is turned into heat in R

Wheatstone bridge, meter bridge, potentiometer Class 12

Balance of the bridge: P/Q = R/S, so S = QR/P (no current through G)
Meter bridge: R/S = l/(100 − l); S = R(100 − l)/l
Potential gradient: k = V_wire/L = IR_w/L (volt per metre)
Balance on the wire: E = kl; E₁/E₂ = l₁/l₂
Internal resistance: r = R(l₁ − l₂)/l₂

Ammeter, voltmeter and their errors Class 12

Shunt for an ammeter: S = I_gR_g/(I − I_g); R_A = R_gS/(R_g + S)
Series resistance for a voltmeter: R = V/I_g − R_g; R_V = R_g + R
Voltmeter across R only: V/I = RR_V/(R + R_V), a little too small
Voltmeter across R and the ammeter: V/I = R + R_A, a little too large

Cells in a battery, maximum power Class 12

n cells in series: E_eq = nE; r_eq = nr
m cells in parallel: E_eq = E; r_eq = r/m
n in series, m rows in parallel: E_eq = nE; r_eq = nr/m; I = nE/(R + nr/m)
Power in the load: P = E²R/(R + r)²; greatest when R = r, P_max = E²/4r
Efficiency: R/(R + r), which is 50% at maximum power

Resistivity and drift velocity Class 10 & 12

Resistance of a wire: R = ρL/A, A = πd²/4
Temperature: ρ(T) = ρ₀[1 + α(T − T₀)]
Current and drift speed: I = nAev_d
Drift speed and mobility: v_d = eEτ/m; μ = v_d/E = eτ/m
Resistivity from the electrons: ρ = m/(ne²τ)
Ohm's law (microscopic): J = σE, with σ = 1/ρ