A novel numerical method has been developed that incorporates electrically conducting objects into particle-in-cell simulations of electrostatic plasma. The method allows multiple objects connected by voltage and current sources in an arbitrary circuit topology. Moreover, by means of an unstructured mesh, the objects can have arbitrary shapes. The electric potential of the objects is solved self-consistently by incorporating charge constraints into the finite element discretization of the Poisson equation. This method has been implemented in a new code, Particles-in-Unstructured-Cells (PUNC), suitable for rapid prototyping. The flexibility of this code has proven convenient to survey various methods, and an issue of reduced convergence rate of today's unstructured plasma-object interaction codes is highlighted. The results for a conducting sphere immersed in the Maxwellian plasma are in good agreement with previous studies.