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Electromotive force (EMF) is often misunderstood as a synonym for voltage, yet it represents the ideal potential difference a battery can deliver when no current flows. By accounting for a battery’s internal resistance, EMF provides a more accurate measure of its true energy‑per‑charge capability.
Use the formula ε = V + Ir where V is the terminal voltage, I the load current, and r the battery’s internal resistance.
EMF is the voltage produced by a cell when no external circuit is connected. In practice, every battery has a non‑zero internal resistance that drops voltage under load. EMF represents the maximum potential difference achievable, so it is always greater than the terminal voltage measured while current flows.
There are two common formulations:
1. ε = E / Q – the energy (E) delivered per unit charge (Q). This definition is useful when you know the total energy output and the total charge passed.
2. ε = I (R + r) – derived from Ohm’s law. Expanding gives ε = IR + Ir = V + Ir, linking EMF to the measured terminal voltage (V), load current (I), and internal resistance (r).
Consider a battery connected to a 3.2 V load, drawing 0.6 A with an internal resistance of 0.5 Ω:
ε = V + Ir = 3.2 V + (0.6 A)(0.5 Ω) = 3.5 V.
Thus, the EMF of the battery is 3.5 V.
