Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2021 / Paper 1 / 11 / iii

If the voltage were held at $4.57\mathrm{V}$ for the entire ideal discharge, thenand the electrical power would beThese are constant-voltage estimates, not a determination of the actual energy from the fresh-cell open-circuit voltage. Under load the voltage depends on state of discharge, electric polarization and internal resistance. The physical result is $E=I{\int }_0^{t_f}{V}_{\mathrm{load}}(t)dt$, and $P(t)=I{V}_{\mathrm{load}}(t)$. The supplied single open-circuit value does not specify that voltage curve; practical delivered energy will generally be lower than the simple estimate.

Increase the electrochemically accessible area and reduce transport resistance rather than merely forcing more electric current through the same thick electrode. A thinner, porous composite distributed over a larger area, a conductive-carbon network, good electrolyte wetting and short ionic paths reduce local current density and electric polarization. Adequate battery separator conductivity and low-resistance collectors also help. Parallel cells can distribute total electric current while retaining the total active-material inventory.

The objective is to preserve usable capacity at a higher rate by avoiding premature voltage cutoff and inaccessible active material. It does not create more charge: a fixed inventory with $175.2\mathrm{Ah}$ delivers a greater electric current for a proportionally shorter time. Maintaining the original two-year duration at greater electric current requires proportionally more capacity.