Question

find the equation of current for RLC circuit using the Bernoulli equation of 1st order. R=1,L=1,C=1,V=28

Answer 1

The magnitude of a current for a series circuit (in case the voltage is constant) is

$$I=\frac{V}{\sqrt{R^2+\bigg(\omega L-\frac{1}{\omega C}\bigg)^2}}.$$

The Bernoulli equation for constant voltage and series circuit is

$$\frac{\text{d}^2I(t)}{\text{d}t^2}+\frac{R}{L}\frac{\text{d}I(\text{d}t)}{t}+\frac{1}{LC}I(t)=0,\\\space\\ \frac{\text{d}^2I(t)}{\text{d}t^2}+\frac{\text{d}I(\text{d}t)}{t}+I(t)=0.$$