Question

What is the internal resistance of a 12.0-v car battery whose terminal voltage drops to 8.4 v when the starter draws 70 a ?

Answer 1

The relationship betwen terminal voltage and electromotive force of a battery is given by:
$V=\epsilon - Ir$
where
V is the terminal voltage
$\epsilon$ is the electromotive force
I is the current
r is the internal resistance of the battery

In our problem, V=8.4 V, $\epsilon=12.0 V$ and the current drawn is $I=70 A$, so we can find the internal resistance of the battery by re-arranging the previous equation:
$r= \frac{\epsilon-V}{I}= \frac{12.0 V-8.4 V}{70 A}=0.051 \Omega$