Analysis of LCR Circuits Using Differential Equations Transient and Steady State Solutions

In programmes 4 and 5 we learnt how to analyse LCR circuits which were energised by alternating current and voltage generators. The analysis depended, however, on the assumption that the generators had been connected to the circuits for some time and that any transient phenomena apparent shortly after the initial connection had been made had had time to die away. The analysis was thus a ‘steady state’ analysis. It is often important, however, to know what happens in a circuit soon after switch-on. Furthermore, generators with outputs which are not sinusoidal are frequently encountered. At the beginning of programme 4 we analysed square waves. Such waveforms are very important and are widely used in ‘switching circuit’ design.