A Comparative Solution using Laplace Transform method on Kirchhoff Second Law with Angular Frequency Effect

This study shows the unique solution to a second-order non-homogeneous linear differential equation using the Laplace transform method with two mathematical models for the sum of voltage drop across the R-L-C circuit with required boundary conditions. Solutions for the charge flowing across the circuit were obtained using the Laplace transform with parameters such as Inductance L, resistance R, capacitance C, Electromotive force (EMF) and angular frequency, all having an effect on the total charge flowing across the circuit. The results obtained showed that the increase in the capacitance and EMF increased the electric charge flowing across the circuit. The presence of the angular frequency in the second mathematical model decreased the electric charge as the resistance increased, when compared to the first Mathematical model, where the electric charge increased. The increase in the inductance increased the electric charge in the second mathematical model when compared to the first mathematical mode,l where the electric charge decreased. The results of the solution from the second mathematical model proved to be better and safer for electrical/mechanical appliances with the effect of angular frequency.