Exercise EE1-02.01 – Electric charge, voltage and energy of a rechargeable battery

Prof. Dr. Thorsten Jungmann (last updated 2025-10-15)

Relates to EE1-02 Electrical quantities and units, terms, symbols and models

Task

A rechargeable battery bears the following manufacturer’s specifications: AA (Mignon), NiMH, 1 600 mAh, voltage 1.2 V.

a) What electric charge $Q$ does the fully charged rechargeable battery store?

b) What is the theoretical charging time of the rechargeable battery at a charging current of $I=400\mathrm{mA}$?

c) At a discharge current of $I=80\mathrm{mA}$, how long does it take until the rechargeable battery has discharged by $70\%$?

d) How many electrons are then still stored in the rechargeable battery?

e) What mechanical work could a remote-controlled car with an efficiency of $50\%$ do if it is powered by a rechargeable battery pack with a rated voltage of $4\cdot 1.2\mathrm{V}=4.8\mathrm{V}$ and four fully charged rechargeable batteries of the type mentioned above, and if the entire stored energy were delivered?

Solution

a) $5760\mathrm{C}$
b) $4\mathrm{h}$
c) $14\mathrm{h}$
d) $\approx 1.08\cdot 10^{22}$ electrons
e) $13.8\mathrm{kJ}$

▶️ Full worked solution