Question

Your father bought a car battery that has a terminal voltage of 12.6V for 75.0A, and 14.1V for 60.0A. What is the electromotive force and internal resistance of this car battery that your father bought?

Answer 1

The Ohm's law says

$$I_1=\frac{\cal E}{R_1+r}$$

$$I_2=\frac{\cal E}{R_2+r}$$

or

$$I_1=\frac{\cal E}{V_1/I_1+r}$$

$$I_2=\frac{\cal E}{V_2/I_2+r}$$

We get

$$75=\frac{\cal E}{12.6/75+r}$$

$$60=\frac{\cal E}{14.1/60+r}$$

Roots:

$$r=0.1\Omega, \;\cal E=20.1\:\rm V$$