We investigate the effect of an applied electric potential on the mechanics of a coarse grained POPC bilayer under tension. The size and duration of our simulations allow for a detailed and accurate study of the fluctuations. Effects on the fluctuation spectrum, tension, bending rigidity, and bilayer thickness are investigated in detail. In particular, the least square fitting technique is used to calculate the fluctuation spectra. The simulations confirm a recently proposed theory that the effect of an applied electric potential on the membrane will be moderated by the elastic properties of the membrane. In agreement with the theory, we find that the larger the initial tension the larger the effect of the electric potential. Application of the electric potential increases the amplitude of the long wavelength part of the spectrum and the bending rigidity is deduced from the short wavelength fluctuations. The effect of the applied electric potential on the bending rigidity is non-existent within error bars. However, when the membrane is stretched there is a point where the bending rigidity is lowered due to a decrease of the thickness of the membrane. All these effects should prove important for mechanosensitive channels and biomembrane mechanics in general.