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The paper presents an analytical analysis of the steady state current-voltage characteristics of corona discharges in point-plane electrode configurations. The paper also discusses the dynamic impulse characteristics of corona discharges based on the solution of the Poisson and the continuity equations which includes the displacement current due to time-varying electric field. The hyperboloid approximation is used to describe the IV characteristics of corona discharges. The best fit of analytically calculated IV curves to experimental data provides the value of the mobility for the charge carriers in the corona discharge. The results of this work provides a greater understanding of the behaviour of corona and will assist with the operational analysis of impulsive pre-breakdown processes in point-plane electrode topologies in electron-negative gases These topologies are important as they are employed in corona stabilised plasma closing switches.