The overall efficiency of a battery can be regarded as:

in which  and  are the discharged and charged energies of the battery. A simple experiment is designed in which a battery cell is discharged and charged again in a controlled manner. Energy is given to a consumer from a battery at a constant current I during time . At this time period, the voltage of battery remains a constant V. Then the battery is charged at the same voltage V, current I and time : (a) Derive an equation for the overall efficiency of the battery. (b) For a battery with open terminal voltage of 11.2 V and internal resistance of 0.05 ohm, plot the efficiency of battery for different currents.