Special singularity integrals encountered in electric circuits [RLC circuit examples]

In this article, the authors first introduce four special singularity integral identities that involve the impulse, the doublet and the unit step functions, and provide a simple proof for each integral identity. Next, to demonstrate the use of these singularity integral identities, the authors consider the impulse response of two second-order RLC circuits and use these integrals to calculate the energy stored and dissipated in each circuit. The authors believe that these solutions are direct and easy to use in electrical circuit problems involving singularity functions. They hope that a wider coverage of these special integral identities and their applications will be offered in the educational literature.