Energy Delivered by a Battery

A battery's voltage, its EMF, is defined as energy per unit charge: joules per coulomb. That's why you don't just quote a battery's energy output in joules alone — the number of joules depends entirely on how much charge you push through it, which depends on the circuit. The voltage is the fixed thing the battery contributes; multiply it by the charge that actually moves, and you get the energy actually delivered.

Follow one coulomb around a loop. Inside the battery, chemical reactions do work on that charge, lifting it to higher potential energy — that input is the EMF. As the charge travels through the external circuit, it loses that potential energy crossing each resistor, converted into heat (and light, if there's a bulb). By the time the charge returns to the battery's other terminal, it has given up essentially all the energy the battery gave it. Over time, charge flows at rate I (current), so energy delivered per second is power, P = IV. Multiply by total time to get total energy: E = IVt.

In a series loop, every resistor carries the same current, but each has a different voltage drop (V = IR for that resistor). Since power delivered to a resistor is I times that resistor's voltage drop, the battery's total power IV splits among resistors in proportion to their resistance — bigger resistors dissipate more power. This connects directly to why a battery doesn't supply one fixed current: current depends on whatever total resistance it's driving. The next step, Kirchhoff's rules, formalizes how voltage drops and currents distribute around more complicated circuits.