A wire's resistance is set by its material and its shape, R = ρL/A. Drag the sliders below to change the length, cross-sectional area and temperature, switch between five metals, and watch the resistance, conductance and the current at 12 V respond in real time.
This simulator turns R = ρL/A from a line of algebra into an object you can reshape. Each control feeds one part of the equation, and one readout answers first, so you can isolate exactly what does what. The five material buttons set the resistivity ρ; the Length slider stretches the wire; the Cross-section slider fattens or thins it; and the Temperature slider warms the metal, nudging its resistivity upward.
Move any one of them and the panel updates together. Drag Length to the right and the wire on the canvas grows longer while the resistance climbs in step — double the length, double the resistance — and because the supply is pinned at 12 V, the current readout drops by the same factor. Drag Cross-section instead and the wire visibly thickens while the resistance falls as 1/A; the conductance readout, being simply 1/R, rises as its mirror image. Switch from copper to nichrome and the resistance leaps about sixty-five-fold without the wire changing shape at all, because only ρ has changed. What the numbers prove, live, is that resistance is never one property — it is material and geometry multiplied together.
The slider that corrects the deepest misconception is Cross-section. It is tempting to think a thicker wire “pushes back” harder, but the simulator shows the opposite: more cross-sectional area gives charge more room to move, so a fatter wire resists less, not more. That is why household cables rated for heavy current are thick, and why a thin filament in a bulb runs hot. To put exact numbers to any wire, use the resistivity calculator or the Ohm's Law calculator; for the full theory read What Is Electrical Resistance? and the companion guide to Ohm's law, or open another model from the full simulation collection.
It changes the wire's cross-section — how thick it is when you cut straight across it — measured in square millimetres. In the formula R = ρL/A, the area A sits on the bottom, so a bigger cross-section means a lower resistance. Watch the wire on screen grow fatter as you drag the slider right, and the resistance readout falls in inverse proportion: double the area and the resistance halves.
Because resistance is proportional to the material's resistivity, and nichrome's resistivity is about 1.1e-6 ohm-metres against copper's 1.68e-8 — roughly sixty-five times larger. Keep the length, area and temperature fixed, switch the metal from copper to nichrome, and the resistance leaps by that same factor of about 65. That huge resistivity is exactly why nichrome is used for heating elements and copper for wiring.
The simulator drives the wire from a fixed 12 V supply, so the current follows I = V/R. Lengthening the wire raises its resistance (R is proportional to length), and a larger resistance at a fixed voltage means a smaller current. Drag the length slider and watch the two readouts move in opposite directions — R up, I down — a direct picture of Ohm's law at a constant voltage.
It models how a metal's resistivity rises as it heats up, using rho(T) = rho20 · (1 + alpha·(T - 20)), where rho20 is the resistivity at 20 degrees Celsius and alpha is the material's temperature coefficient. Raise the temperature and the resistivity — and therefore the resistance — climbs for all five metals, which is why an incandescent bulb's filament has a far higher resistance when glowing hot than when cold.
Yes. Conductance G is the reciprocal of resistance, G = 1/R, measured in siemens (S). It is simply the other way of describing the same thing: a low-resistance wire is a high-conductance wire, and vice versa. The simulator shows both so you can see them move as mirror images — anything that lowers R raises G by the same factor.