internal resistance
Summary
Internal resistance (r) is the resistance inside a real battery that makes its terminal voltage lower than its emf when it delivers current. Terminal voltage is V = ε − Ir, so it falls as current rises and equals the emf when no current flows.
Detail
Meaning: A real battery behaves like an ideal emf source ε in series with a small resistor r. Current through the battery loses some potential across r, so the voltage available to the external circuit, the terminal voltage, is less than ε. Energy is also dissipated as heat in r at a rate I²r.
Equation: V = ε − Ir, where V is terminal voltage (V), ε is emf (V), I is current through the battery (A), and r is internal resistance (Ω). With an external load R, I = ε/(R + r).
On the MCAT: A passage gives a battery with emf and r connected to a load. Find I from ε/(R + r), then V. Predict that lowering the load resistance, for example by adding resistors in parallel, raises I and lowers V. A short circuit gives the largest current, ε/r. When a battery is being charged, the sign flips: V = ε + Ir.
Common confusion: Students assume a battery's terminal voltage equals its labeled emf. For a real battery that is true only in the open-circuit case, where I = 0. A voltmeter across a battery in a working circuit reads less than ε. Also, r is in series with the load, not in parallel with it.
Sources
- Physics (Cutnell and Johnson)
- University Physics (Young and Freedman)
- Physics (Giancoli)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.