Potential Difference Simulator

What Is the Potential Difference Simulator?

Watch the Volts Split — and Refuse to Vanish

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.

Where the ideal potential divider breaks down

Start with the supply. Whatever load you hang on it, this source holds the voltage you dialled: push both resistances to 1 Ω at 24 V and the readout reports 12.000 A with the supply sitting unmoved. No real cell does that. Every source carries internal resistance in series inside its own case, so the terminal p.d. sags to V − I·r as soon as current flows. Read R1 as that internal resistance and the simulator shows you the size of it: at 24 V with R1 = 1 Ω and R2 = 50 Ω, the load receives only V2 = 23.529 V, and the missing 0.471 V is burnt inside the battery. That resistance climbs as a cell discharges, which is why a nearly-flat battery reads full on a meter and dies under load.

The connecting wires have no resistance at all here, so the staircase runs dead flat between the resistors. Real copper, connectors, solder joints and a corroded earth strap each add a fraction of an ohm, and the loop rule treats them like any other resistor: they take their share of the volts. That is why a long thin extension lead leaves a heater running cool, and why a dim headlight is usually a bad earth rather than a bad bulb.

The resistances are frozen too. Set 24 V across two 1 Ω resistors and the sim reports 12.000 A quite cheerfully — but 12 A through 1 Ω is I²R = 144 W in each resistor, hundreds of times what a quarter-watt component survives. Well below that limit resistance still drifts as a component warms, so a divider trimmed to the right split cold no longer holds it after a minute under load.

And a divider only divides while nothing is connected to the middle of it. Tap the junction between R1 and R2 to drive something, and whatever you connect sits in parallel with R2, drags the pair's combined resistance down and shifts the split away from your calculation. That is also why a voltmeter is built with an enormous internal resistance: to disturb the p.d. it is reading as little as possible.

Finally, the charge sliding down the staircase is a picture, not a mechanism. Carriers in a real wire drift at well under a millimetre per second while the energy arrives through the fields around the conductor. V = W/Q averages over an enormous population of carriers; it does not follow one of them.

Where this is actually used

Almost every microcontroller that measures its own battery uses this circuit. A 3.3 V chip cannot take 12 V on an input pin, so a divider scales the reading first. Set the supply to 12 V, R1 to 33 Ω and R2 to 12 Ω: the sim gives I = 0.267 A and V2 = 3.200 V, safely inside a 3.3 V input. The real board uses 33 kΩ and 12 kΩ instead — the ratio, and therefore the 3.200 V output, is identical, but the current falls a thousandfold, so the divider does not flatten the battery it monitors.

Turn the circuit around and it becomes a current meter. Put a small known resistance in series with a load and the p.d. across it reads the current directly. Set 5 V with R1 = 1 Ω and R2 = 9 Ω: V1 shows 0.500 V, and because R1 is exactly 1 Ω that figure is also the current, 0.500 A, which is what the I readout says. The cost sits in the same panel — the sense resistor has claimed 0.500 V of the 5 V, a tenth of the supply. Real shunts are milliohms for exactly that reason.

Swap R2 for something whose resistance tracks the world and the divider becomes a sensor. A car's coolant temperature sender is a thermistor in a divider on a steady 5 V rail, and the engine computer reads the junction voltage rather than the resistance. Hold R1 at 10 Ω on a 5 V supply and move R2: at 50 Ω the output V2 is 4.167 V; at 2 Ω it has fallen to 0.833 V.