Internal Resistance Calculator (EMF & Terminal Voltage)

How it works

ε = V + I·r · I = V/R → r = (ε − V)/I = R·(ε − V)/V · short-circuit current I_sc = ε/r · maximum power P_max = ε²/(4r) when R = r · efficiency η = V/ε = R/(R + r)

Every real source — a battery, solar cell or power supply — behaves like an ideal EMF in series with a small internal resistance. When current flows, part of the EMF is dropped inside the source (the “lost volts”), so the terminal voltage falls below the open-circuit value. Measuring the voltage with and without a known load gives the internal resistance directly. The maximum power transfer theorem says a load extracts the most power when it matches r, but efficiency is then only 50%. Method as in OpenStax University Physics Vol. 2, section 10.1.

Worked example

A battery reads 12 V on open circuit and 11.4 V with a 2.85 Ω load. The current is 11.4 / 2.85 = 4.000 A, so r = (12 − 11.4) / 4 = 0.1500 Ω. The load receives 45.600 W while 2.400 W is lost inside the battery (95.00% efficiency). A dead short would draw 12 / 0.15 = 80.00 A, and the most power any load could take is 12² / (4 × 0.15) = 240.00 W.

Sources: OpenStax University Physics Vol. 2 — Electromotive Force · HyperPhysics — Internal resistance of a battery

Frequently asked questions