terminal voltage
/ TER-mih-nal VOHL-tij /
Terminal voltage is the voltage you would actually measure across a battery's two terminals right now, as opposed to the ideal push it advertises. Think of a water pump rated for a certain pressure: when it is idle the gauge reads the full pressure, but as soon as water gushes out, friction inside drops the reading. Terminal voltage is that real, present reading. It answers the question: how much voltage is this source truly delivering to my circuit at this moment?
Precisely, the terminal voltage V is the potential difference between the source's terminals when a current is being drawn. It differs from the EMF by the drop across the internal resistance r: while a battery discharges, V = EMF - I r, so the terminal voltage sinks below the EMF as the current I rises. When the battery is charging instead, current is forced backward through it and the terminal voltage climbs above the EMF, V = EMF + I r. Only at open circuit, with I = 0 and no current flowing, does the terminal voltage equal the full EMF.
Terminal voltage is what your devices actually feel, so it, not the EMF label, decides whether a gadget runs properly. It explains why a 12 V car battery might read only 10 V while cranking, why a flashlight dims as its cells tire, and why measuring a battery under load reveals its true health far better than an idle reading. One honest caveat: a voltmeter reads terminal voltage, not EMF; to find the EMF you must measure with essentially no current flowing, or account for the I r drop.
A phone battery of EMF 3.8 V and internal resistance 0.1 ohms delivering 2 A shows a terminal voltage of V = EMF - I r = 3.8 - 2 x 0.1 = 3.6 V. Left idle with no current, its terminals would read the full 3.8 V.
Terminal voltage equals EMF minus the internal I r drop; it only equals EMF at open circuit.
A voltmeter reads terminal voltage, not EMF. The two are equal only when no current flows; under load the terminal voltage is always less (or, while charging, more) than the EMF.