Internal Resistance and Terminal Voltage

Every real battery is made of chemicals and metal that resist current just like any other conductor. This internal resistance, r, sits in series with the ideal emf source inside the battery, whether you draw the circuit that way or not. When current I flows, the battery itself eats a voltage Ir, the same way any resistor would. What's left for the rest of the circuit is the terminal voltage: V = emf - I r. At rest, with no current flowing, V equals emf exactly, which is why a battery reads its labeled voltage on a voltmeter when nothing is connected.

The bigger the current demand, the bigger the bite internal resistance takes. A starter motor draws a huge current for an instant, so Ir grows large and the terminal voltage sags, starving the headlights on the same battery of their usual voltage, which is why they dim. The same logic sets a ceiling on how much power a battery can deliver: power delivered to an external resistor R is I² R, with I = emf / (R + r). Maximizing that expression over R shows the external resistance draws maximum power when R equals r, a result worth remembering as a clean, testable fact about any source with internal resistance.

This sits right next to Kirchhoff's voltage law: internal resistance is just one more IR drop to add into the loop equation, treated exactly like any series resistor. It also previews why real circuits never reach the idealized efficiency of a perfect emf source, a theme that returns when power dissipation and circuit efficiency come up later in the unit.