Three-walled boron & nitride nanotubes are used for a theoretical study of a cylindrical molecular capacitor, including an inner cylinder with a positive charge distribution and an outer cylinder with a negative charge distribution. Due to the semiconductor characteristic and dielectric functionality of SWBNTs, DWBNTs and TW (B&C) NTs can be used as a capacitor. Although the SWBNTs @ SWCNTs behave like Nano cylindrical capacitors, we have shown in this study that a dopant of BN in the inner cylinder reduces the energy gap and yields a better capacitance. The dopant of BN in the outer cylinder results in an inverse charge distribution (outer is positive and inner is negative). Therefore under these circumstances, the term capacitor would be meaningless, thought, the gap and the interaction energy decreases compared to the non-dopant form of those capacitors. Density functional theory (DFT) calculations have performed for the structure and stability of three wall carbon Nano tubes (TW (BN&C) NTs). In this work, it was calculated the geometrical structure, and stability to predict NMR and thermodynamics parameters. A mixing of SWBNNTs @ DWCNTs has been modeled and calculated for the suitable structures to storage the H2 molecules for increasing the dielectric. We have found these kinds of Nano-structures are useful for maximum storages of charges compare to other cylindrical capacitor.