The calculation of the conductance of closed ballistic rings requires a theory that goes well beyond the Kubo-Drude formula [S. Bandopadhyay, Y. Etzioni and D. Cohen, Europhys. Lett. 76, 739 (2006)]. To realise the ballistic case we use a single scatterer, characterised by the total transmission gT , in the ring. Assuming mesoscopic circumstances of very weak environmental relaxation, the conductance is much smaller compared to the naive expectation. Namely, the electromotive force induces an energy absorption with a rate that depends crucially on the possibility to make connected sequences of transitions. Thus the calculation of the mesoscopic conductance is similar to solving a percolation problem. The percolation is in energy space rather than in real space. Non-universal structures and sparsity of the perturbation matrix cannot be ignored. The latter is implied by a lack of quantum-chaos ergodicity in ring shaped ballistic devices. Our study also distinguish between the initial transient response (spectroscopic conductance) and the long-time steady state response (mesoscopic conductance) [Y. Etzioni, S. Bandopadhyay and D. Cohen, cond-mat/0607746]. The mesoscopic conductance may be larger than Landauer conductance depending on number of open modes M and the level-broadening parameter . This way, our study goes beyond Landauer.