How this instrument works
Voltage does not flow. It is a difference — the potential energy each coulomb of charge surrenders in crossing a component, measured across that component rather than through it. Resistance sets the exchange rate. Push one ampere through one ohm and every coulomb gives up one joule, which is precisely what a volt is, and multiplying those two quantities gives you the drop. That product is all of V = I·R.
Georg Simon Ohm published this in an 1827 Berlin monograph, Die galvanische Kette, mathematisch bearbeitet. His decisive experimental move was abandoning the voltaic pile, whose output sagged as it discharged, in favour of thermocouples held between boiling water and melting ice — sources steady enough to trust across long afternoons of readings. German academic reception was hostile enough that he resigned his teaching post at Cologne; vindication came slowly, via the Copley Medal from London's Royal Society in 1841 and his name fixed to the unit by an electrical congress in Paris in 1881. Henry Cavendish had reached much the same relation around 1781 by running charge through his own body and grading how badly it hurt, then told nobody; Maxwell published those notebooks in 1879, fifty years too late to matter.
Read it as shorthand for well-behaved materials rather than as physical law. Ohmic conductors — copper wire, carbon film resistors, nichrome at steady temperature — hold R fixed while current varies. Many components refuse: diode resistance collapses once past its forward voltage, tungsten lamp filaments run ten to fifteen times more resistive hot than cold (hence the large switch-on surge, and why bulbs die at the flick of the switch rather than mid-evening), and thermistors exist specifically to disobey. Quote one R value for parts like those and you have quoted it at one operating point only.
- Type your figure into Current. The unit menu accepts milliamps and kiloamps too, so a 20 mA signal needs no hand conversion.
- Enter Resistance in ohms, or switch its unit to kΩ, MΩ, or mΩ to match whatever is printed on the part or read off a meter.
- Read Voltage, returned to four figures. Flip its unit to mV or kV when that suits the scale you are working at.
- Check the answer against your actual supply — a drop exceeding the source voltage means the current figure came from somewhere wrong.
Worked example — one amp through one ohm
Wire a bench supply across a single 1 Ω power resistor and trim it until your ammeter settles on 1.000 A. Enter 1 into Current and 1 into Resistance; Voltage returns 1, since 1 × 1 = 1 volt appears across that part. Round numbers are not luck here — an ohm is defined as whatever resistance drops one volt per ampere, so this case pins down its meaning.
That resistor will confirm it thermally as well. At 1 A and 1 V it dissipates exactly 1 watt, plenty to make a quarter-watt film part smell of scorched lacquer inside a few seconds. Scale both inputs and arithmetic stays friendly: 20 mA through 1 kΩ also lands on 20 V, because milli and kilo cancel each other out.
Questions
Is Ohm's law really a law?
Not in a way conservation of energy is. It captures how linear materials behave, and plenty of components are not linear — semiconductors, gas discharges, electrolytes, anything that heats appreciably under load. A safer reading: V = I·R defines resistance at one operating point, and calling something ohmic asserts how wide a range that point holds over.
What is the difference between voltage across and current through?
Voltage gets measured across a component, current through it — swapping those two is a classic bench error. Your voltmeter sits in parallel, touching both ends of a part, and draws almost nothing. An ammeter must be spliced into the path so every electron passes through it. Clip an ammeter straight across a supply and you have placed a near short circuit there, which is how meter fuses meet their end.
Why does my measured resistance drift with temperature?
Resistivity depends on temperature in nearly every conductor. Copper climbs about 0.4% per degree Celsius, so a motor winding checked warm after a run reads several percent above its cold value — exactly how test labs infer winding temperature without a probe. Tungsten is extreme, rising by an order of magnitude between a cool room and 2500 K. Precision parts use alloys such as manganin, picked because that coefficient sits near zero.
How do I get power from these numbers?
Multiply: P = V·I, in watts. Substituting V = I·R yields two forms engineers reach for constantly, P = I²R and P = V²⁄R. Power decides survival — 1 A through 1 Ω makes 1 W, destroying a 0.25 W film resistor while a 5 W wirewound barely warms. Resistance tells you what voltage appears; power tells you which package can take it.
Is voltage or current what makes a shock dangerous?
Current does harm, though voltage drives it, so neither stands alone. Roughly 1 mA is perceptible, 10 mA can clamp muscles so a grip cannot be released, and 100 mA across a chest risks fibrillation. Dry skin may offer 100 kΩ, holding a 230 V supply to about 2 mA; wet hands can drop near 1 kΩ, and an identical supply then pushes a lethal figure. What changed was R, not any principle.
Does it still apply to alternating current?
In this exact form, only for pure resistance. Add capacitance or inductance and resistance generalises to impedance Z, so V = I·Z carries a phase angle alongside its magnitude — capacitor current leads voltage, inductor current lags. For a kettle element or an incandescent lamp on mains, though, plain real-valued arithmetic on RMS values remains perfectly sound.