Thevenin Equivalent Circuit Question
Imagine one of many loads can be applied. What is the resulting voltage on the battery?







simulate this circuit &ndash; Schematic created using CircuitLab  &lt;=== ignore

ref   ESR

I have rounded up the current.  Notice one is 50A. Why?

All batteries and power supplies have a series resistance, where rising current , results in a voltage regulation error or drop in voltage.  

Batteries are pretty linear and a short circuit would  not be safe after a certain time interval due to temperature rise.  Op Amps and Power Supplies will be linear until active current limiting, by design.   

An example of this is a car battery where a fully charged battery is 12.5V and the amount of current at 0'C that can be sustained for 30 seconds at 7.5V is called the Cold Cranking Amps.  This is because   batteries reduce in Ah and rise in ESR near and below freezing. 
thus $$Vbat=Voc - I*ESR$$

Test

So for a 5V drop what is the series resistance , Rs or ESR if the CCA=750 A?
( I don't use Rth)

Example 2

A solar PV has Voc= 12V and a short circuit current of 1.2A  what is the maximum power operating point and max power?  Assume the PV is a nonlinear current source but ideal between short and open circuit.  Hint what is the PV Impedance at full solar input?  What is the max load power resistance? (if you know MPT theorem)