Potential difference (voltage) is the energy given to each coulomb of charge, V = W/Q. Drag the sliders below to set the supply p.d., the two resistances and the charge, and watch the volts drop step-by-step down a series circuit — the drops always adding back to the supply.
This simulator draws a series circuit as a potential staircase. A charge begins at the top, holding the full supply potential, then steps down across each resistor until it reaches zero volts at the far terminal. Every slider reshapes that staircase in a different way, and reading them together is the fastest route to understanding what voltage really is.
The Supply p.d. slider sets the height of the whole staircase. Raise it and the shared current climbs with it, so both drops — V1 across R1 and V2 across R2 — grow in proportion while their sum tracks the supply exactly. The R1 and R2 sliders redistribute the same total between the two steps: increase R1 and it seizes a bigger share of the volts, which forces V2 down by precisely the amount V1 gained. Under the hood the sim does what any circuit solver does — it computes the current from I = V/(R1+R2), then applies V = IR to each resistor — so the readouts you see are the loop rule and Ohm's law working together.
The Charge slider is the one that overturns a stubborn misconception. Drag it and the energy each resistor absorbs, W1 and W2, scales straight up — yet every voltage on the panel refuses to budge. That is because the V1 + V2 readout is not measuring a hoard of volts being spent; it is Kirchhoff's voltage law made visible, the guarantee that the drops always re-sum to the supply. Voltage is energy per coulomb, so pushing more coulombs through moves more joules without changing the ratio. Once that clicks, the definition V = W/Q stops being a formula to memorise and becomes something you have watched hold true. Put numbers to it with the potential difference calculator, read the full theory in What Is Potential Difference (Voltage)?, connect it to current and resistance via Ohm's law, or open another model from the full simulation collection.
Because potential difference is energy per unit charge, V = W/Q, not energy alone. When you drag the charge slider, the energy each resistor takes (W1 and W2) scales up in exact proportion, so the energy-per-coulomb ratio — the voltage — stays fixed. That is the whole point: voltage is not a stock that gets used up as more charge flows; it is a property of the two points, the same for one coulomb or a thousand.
The circuit is in series, so a single current flows through both resistors: I = V/(R1+R2). Raising R1 increases the total resistance, which lowers that shared current. A bigger R1 with a smaller current still claims a larger share of the supply (V1 = I·R1 rises), and because the two drops must add to the fixed supply, V2 = I·R2 falls by the same amount. The split shifts, but the total never changes.
It is Kirchhoff's voltage law — the loop rule — made visible. However you set the resistances, the two potential drops always sum to the supply p.d., because a charge that climbs to the supply potential must give all of that energy back by the time it returns to the negative terminal. The readout stays glued to the supply voltage no matter how you move the sliders.
No — this simulator models two resistors in series, sharing one current and splitting the supply voltage between them. In a parallel arrangement each branch instead sees the full supply voltage while the current splits between the branches, so the maths is different. Use this lab to master the series loop rule first; the ideas transfer once the series case is clear.
It solves the series circuit in two steps. First it finds the current from the supply and the total resistance, I = V/(R1+R2). Then it finds each potential drop with V = IR, giving V1 = I·R1 and V2 = I·R2. Finally the energy each resistor takes from a charge Q is W = QV, and dividing energy by charge returns the voltage, confirming V = W/Q.