How to find a battery's internal resistance given load resistance and change in terminal voltage?

Question

The question is:

Suppose we measure the terminal voltage of a rechargeable NiCad battery and find it to be 1.28 V when measured by a voltmeter. We now connect a 8.0-ohm resistor across the terminals, and find that the terminal voltage has now changed, to 1.16 V. Find the internal resistance of the battery in ohms.

Answer 1

In this case, what you measure without any external resistance is the electromotive force of the battery, E. When current starts to flow, the terminal voltage becomes V which is lower than E. If Current I is flowing, R is external resistance and r is internal resistance, then,

E = I (R+r) = IR + Ir = V + Ir

therefore, r = (E-V)/I and again, I = V/R

Therefore, r = (E-V)*R/V.

In your case, (1.28-1.16)*8/1.16 ohm = 0.828 ohm