Internal Resistance of a Battery

Question

You connect unknown resistors across the terminals of a battery and take the following measurements:

1. Terminal Voltage 14V, Current 4A
2. Terminal Voltage 10V, Current 20A

a) What is the internal resistance of the battery?

b) What is the emf (open circuit) voltage of the battery?

c) What is the maximum (short-circuit) current the battery can deliver?

d) What are the resistances of the resistors you used for this test?

Answer 1

First draw the two circuits as Thevenin circuits.

Using Ohm's Law yields these two linear equations:

(E - 14)/4 = Ri

(E - 10)/20 = Ri

Put in standard form and solve for E = 15V and Ri = .25 ohms

Draw the Thevenin Circuit and by using Ohm's Law solve for Imax, R1 and R2

Answer 2

Let me know if anyone has questions on how to calculate internal resistances of batteries or power supplies for experimentation:

a) Ri = 0.25Ω

b) ε = 15V

c) I_max = 60A

d) R₁ = 3.25Ω, R₂ = 0.25Ω