ANALYSIS OF THE INFLUENCE OF PARAMETERS WHEN CHARGING AND DISCHARGING A CAPACITOR USING DIFFERENTIAL EQUATIONS

Abstract

Two different electrical circuits were analysed in this paper. The first was an RC circuit consisting of a resistor R, a capacitor C, and a DC voltage u, while the second was an RLC circuit consisting of a resistor R, a capacitor C, a DC voltage u and an inductor L. Both circuits were described using the state space mathematical model and, on this basis, graphs for charging and discharging a capacitor were plotted. Both circuits were described using differential equations for electrical current through a capacitor and voltage over a capacitor. Finally, different values of the R (resistance), L (inductance) and C (capacitance) parameters were taken, and graphs were plotted for voltage over capacitor. The purpose of the study was to explore how different values of parameters influence capacitor charging and discharging.V tem članku sta bili analizirani dve različni električni vezji. Prvo je bilo RC vezje, sestavljeno iz upora R, kondenzatorja C in enosmerne napetosti u. Drugo je bilo RLC vezje, ki je bilo podobno prejšnjemu vezju, le da je bila dodana tuljava L. Obe vezji sta bili pretvorjeni v matematični model v prostoru stanj in na podlagi tega so bili izrisani različni grafi za polnjenje in praznjenje kondenzatorja. Obe vezji sta opisani z diferencialnimi enačbami za električni tok skozi kondenzator in napetost na kondenzatorju. Na koncu so bile izbrane različne vrednosti parametrov R (upornosti), L (induktivnosti) in C (kapacitivnosti) in na podlagi tega so bili izrisani grafi za napetost na kondenzatorju. Namen je bil videti, kako različne vrednosti parametrov vplivajo na polnjenje in praznjenje kondenzatorja.