The behavior of eigenvalues of regular matrix pencils under rank one perturbations which depend on a scalar parameter is studied. In particular we address the change of the algebraic multiplicities, the change of the eigenvalues for small parameter variations as well as the asymptotic eigenvalue behavior as the parameter tends to in nity. Besides that, an interlacing result for rank one perturbations of matrix pencils is obtained. Finally, we apply the result to a redesign problem for electrical circuits.