A \"dead\" but rechargeable car battery has an emf of 11.4 V and internal resist

Question

A "dead" but rechargeable car battery has an emf of 11.4 V and internal resistance of 1.14 O. To start the car, a good battery ( = 12.0 V, r ˜ 0) is connected to the dead battery by jumper cables of negligible resistance (see figure below). The battery terminals are connected + to + and - to -. The weak battery is charged by the strong battery when connected in this way.

(a) How long does it take for the weak battery to receive a 2.10 amp-hour charge? Assume that the emfs and resistances remain constant.


(b) How long would it take to acquire this same 2.10 amp-hour charge if the engine were running and the generator were charging the battery with a current of 3.64 A?

Explanation / Answer

(a) current = 12-11.4 / 1.14 = 0.526 A 0.526*t = 2.1 t = 4 hours (b) time taken in that case = 2.1/3.64 = 0.577 hours = 34.62 minutes

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