Final answer:
The calculation based on the provided values gives an internal resistance of 0.375 Ω, which doesn't match any of the given answers, indicating a possible typo in the question. The terminal voltage should not be higher than the EMF under normal discharging conditions, which is a key point of confusion here. none of the options given would be correct.
Step-by-step explanation:
To find the internal resistance (r) of the automobile battery we can use the equation involving the electromotive force (emf), terminal voltage (V), current (I), and internal resistance (r), given by:
emf = V + Ir
Plugging in the values provided:
12.0 V = 15.0 V - (8.00 A × r)
To solve for r, first rearrange the equation:
r = (15.0 V - 12.0 V) / 8.00 A
r = 3.0 V / 8.00 A
r = 0.375 Ω
However, this value doesn't match any of the options provided, suggesting there may have been a typo in the terminal voltage value given for the question. Normally, the terminal voltage should be less than the emf when the battery is discharging, not higher as implied here.
If considering the rare condition when a battery is being charged instead, which would explain a higher terminal voltage, none of the options given would be correct.