Experiment 2: Transients and Oscillations in RLC Circuits

Transient responses of RLC circuits are examined when subjected to both long time scale (relative to the decay time) square wave voltages and sinusoidally varying voltages over a range of frequencies about the resonant frequency. In general, a good correspondence is found between theory describing the charge in the system in terms of a 2nd order differential equation with a harmonic oscillator form and experiment. It is demonstrated that the inductance can be accurately measured using period of oscillation versus capacitance measurements. Furthermore, the exponential decay of the response is described well by the model and the resonant frequency of a sinusoidal external voltage is accurately predicted. However, some discrepancies were found though not necessarily a result of theoretical failures. One problem is the failure to predict the inductance of a circuit based on the critical resistance variation with capacitance, although the problem could lie in how the measurement is conducted. Additionally, the quality and bandwidth of a RLC element is poorly predicted but this could also be a result of experimental problems.