Past exam of the physics 2 paper of the University of Oxford / 2015 resit / 3 / Solution

For a fixed number $N$ of identical bulbs, first approximate each as a resistor of electrical resistance $R$ connected to a fixed ideal battery electric potential difference $V$. A series circuit has electrical resistance $NR$, while a parallel circuit has electrical resistance $R/N$. ThusParallel connection therefore maximizes dissipation in this model: every bulb receives the full source electric potential difference instead of sharing it. For $N=1$ the two arrangements coincide.

An actual incandescent light bulb changes electrical resistance as its filament heats, so a single constant $R$ need not describe both operating points. The same qualitative conclusion holds for identical stable bulbs with increasing current-voltage function $i(U)$: parallel operation gives $P_p=NVi(V)$, whereas symmetric series operation gives $P_s=Vi(V/N)$. The former is larger for $N>1$. This comparison assumes a fixed collection and an ideal source as specified; an unlimited number of parallel bulbs on a zero-internal-resistance ideal battery would have no finite total-power maximum.