Voltage Is Always a Difference, Never an Absolute
The single most useful idea about voltage is that it does not exist at a point. It is a potential difference between two points, which is why a multimeter has two probes and why asking "what is the voltage here?" is incomplete until you say "with respect to what?"
This is the reason ground is defined rather than discovered. Ground is simply the node chosen as the zero reference, and every other voltage in the circuit is quoted relative to it. Choose a different node and every number changes, though the circuit behaves identically.
The three routes to a voltage
| Known quantities | Formula |
|---|
| Current and resistance | V = I × R |
| Power and current | V = P / I |
| Power and resistance | V = √(P × R) |
All three come from Ohm’s law combined with P = VI, so they are consistent with one another; which to use depends only on what you already know.
Why measured voltage is lower than calculated
Real sources have internal resistance, so terminal voltage falls as current is drawn: Vterminal = Vsource − I×Rinternal. A battery reading 12.6 V unloaded may read 11.8 V under a heavy load, and nothing is faulty — that drop is the internal resistance made visible, and it is how battery condition is often judged.
Cable resistance does the same thing along the run. A long low-voltage cable can lose a substantial fraction of the supply voltage, which is why voltage drop, not just current rating, governs cable sizing on extended runs.
AC voltages need their reference stated too
An AC voltage is normally quoted as RMS, the value producing the same heating as an equal DC voltage. For a sine wave the peak is √2 times higher, so nominal 230 V mains actually peaks at about 325 V — which is the figure that matters for insulation ratings and semiconductor breakdown voltages, even though every meter and nameplate quotes 230.