where \(V_{cell}\) is either the reduction potential in forming \(H_2\) or the reduction potential of MtrC, depending on the mode of electron uptake, \(V_{\gamma}\) is the output potential from the photovoltaic cell, \(I_{Cell}\) is the current in the circuit, and \(I_{\gamma}\) is the current from the photovoltaic cell. This can be obtained from the current density of the photovoltaic cell \(\left(J_{\gamma}\right)\)multiplied by the area of the solar panel.
With both \(\text{H}_{2}\)-mediated and EET-mediated electrosynthesis, we consider an upper bound on the efficiency of solar photovoltaic driven electrolysis of water and reduction to either \(\text{H}_{2}\) or MtrC, followed by oxidation of the electron source, \(\text{CO}_{2}\) fixation and fuel synthesis by an electrosynthesic organism. The photovoltaic current source is able to produce maximum power when the external potential difference \(V_{\gamma}\) is \(0.75\,\text{V}\)at a current density of \(430\,\text{A}\,\text{m}^{-2}\) (ref Nelson 2003). However, \(0.75\,\text{V}\) is too low a potential difference to split water and generate \(\text{H}_{2}\) or reduce MtrC, so needs to be transformed to a higher voltage by the transformer in the circuit (Figure \ref{935612}C,D). The voltage required across the cell is