Using circuit theory and solutions of a scalar two-dimensional Laplace equation for the electrostatic potential, we examine various feedthroughs of interest for voltage holding, voltage standing wave ratio (VSWR) and impedance characteristics. Suitable inhomogeneous Dirichlet, scalar boundary conditions are imposed for the potentials for the calculation of the electrostatic fields. The inhomogeneous vector Newman boundary conditions on the surface of the dielectric are dispatched by use of a conformal mapping. Several feedthroughs are examined: old Princeton Large Torus (PLT), JÜLICH designs, and several Oak Ridge National Laboratory (ORNL) designs that have been actually fabricated and exhaustively tested. Some of these feedthrough configurations have been optimized to provide constant 50-Ω impedance or minimum VSWR.