Four quantities describe any resistive circuit — voltage, current, resistance and power — and just two laws tie them together: V = I·R and P = V·I. Enter any two and this calculator solves the other two exactly, so it works as an Ohm's law solver and a volts-amps-ohms-watts converter. Watch the value on a real battery-and-resistor circuit: current flows, the resistor glows with the power it turns into heat, and the I–V line shows the straight-line proportionality whose slope is 1/R. It all runs on your device.
You are in the Physics lab.
What the circuit, the glow and the I–V line are telling you.
Choose a pair from the I know… menu — voltage and resistance, power and current, any of the six — and type the two values. The readouts show all four quantities at once, with the two you entered in plain type and the two the tool solved shown in the accent colour. Switch pairs and the same circuit is described from a different pair of corners.
Current flows from the battery through the resistor, drawn as chevrons that thicken up as the current grows. Behind the resistor is a heat glow whose size and colour track the power P it dissipates — faint amber for a fraction of a watt, fierce and white-hot for hundreds. It is a direct reminder that power, not resistance, is what heats a component and sets the wattage rating it needs.
The lower graph plots current against voltage for the present resistance. Because I = V/R, it is a straight line through the origin, and its slope is 1/R — a smaller resistor makes a steeper line (more current per volt), a bigger one a shallower line. The green operating point sits where your voltage meets that line. Change the resistance and the whole line pivots.
One proportionality, one power law, and the six ways to enter them.
Ohm's law says the current through a resistor is proportional to the voltage across it, with the resistance as the constant of proportionality: V = I·R. Rearranged, I = V/R and R = V/I. It holds for ohmic components — ordinary resistors and wires at a steady temperature — and it is the backbone every other form is built on.
Power is voltage times current, P = V·I. Substituting Ohm's law gives P = I²·R and P = V²/R, so power follows from any pair of the other three. These three forms are why a fixed resistor can dissipate almost nothing or burn out, depending only on how hard the circuit drives it.
Four quantities linked by two independent equations means two knowns fix the other two. The six pairs each have a clean solution: V,I → R,P; V,R → I,P; I,R → V,P; P,V → I,R; P,I → V,R; and P,R → V = √(P·R), I = √(P/R). This calculator picks the right formula for whichever pair you choose.
Real circuits span a huge range — microamps to hundreds of amps, milliohms to megohms — so the readouts use engineering prefixes (µ, m, k, M) to stay readable. The maths is done in base SI units and only the display is scaled, so a 470 Ω resistor at 9 V reads 19.1 mA and 172 mW, exactly as bench instruments would show.
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