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Battery internal resistance

Batteries and solar · Beginner · about 10 minutes · part of Zen’s Electronics Design Mastery

A real battery is an ideal voltage E in series with a small internal resistance r. With no load you read E. Under load, I · r is lost inside, so the terminal voltage sags and the battery warms up.

Battery internal resistance: the circuit on the simulator's bench

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How it works

E = 9 V, r ≈ 1.5 Ω (a fresh alkaline PP3)

I = E / (r + RL) = 9 / (1.5 + 22 Ω) = 382.2 mA

Vterminal = E − I·r = 8.427 V; lost inside: I²·r = 219 mW

Measure it yourself: r = (Vopen − Vloaded) / I. The short-circuit current is E / r = 6 A, which is why a 9 V battery can’t start a car.

Try it on the bench

  1. Close the load switch and watch V_term drop from 9 V.
  2. Change R_L to 4.7 Ω: the sag gets much worse. Low-resistance loads expose the internal resistance.
  3. Compare with the bench supply, which has about 0.02 Ω inside.

Parts on the bench

In the course

Zen’s Electronics Design Mastery, module “DC Fundamentals”.

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