Question 1.14: For example, let us assume we get a battery that is rated to...
For example, let us assume we get a battery that is rated to provide 12 V in open-circuit mode, that is, no load. Let us further assume that we model such battery to have an internal resistance of 1 Ω. What does this mean?
The internal resistance of the battery is in a way a figure of merit of the battery.
It expresses what can conceivably be the absolute largest current that the battery can supply if its terminals are short-circuited. The battery short-circuit current is given by
Short-Circuit Current I_{shc}=Open-Circuit Voltage V_{oc}/Internal Resistance r_{int}. (1.66)
I_{shc}=V_{oc}/r_{int}. (1.67)
I_{shc}=12 V/1\Omega =12 A. (1.68)
In practical terms, real batteries will not be able to supply their short-circuit current for very long (maybe for just a few seconds if that long). However, the internal resistance inclusion within the ideal voltage source model provides a
touch of realism when modeling the battery. Note that modeling the battery with an ideal voltage source means that the short-circuit current that the source can supply is infinitely large. Inclusion of an internal resistance limits
the current to a finite number. As the battery supplies power to a load, it becomes discharged; which is equivalent to the battery internal resistance to grow in ohmic value as time progresses