I wrote about the idea of ​​representing AC circuits using complex numbers. Consider an RLC series circuit as shown in Figure 1. Now, the instantaneous value of the current flowing through this circuit is $$i(t)=I_m\sin(\omega t-\theta)\hspace{185pt}(1)$$ The instantaneous value of voltage is $$e(t)=Ri(t)+L\frac{di(t)}{dt}+\frac{1}{C}\int i(t)dt\hspace{130pt}(2)$$ $$=RI_m\sin(\omega t-\theta)+L\frac{d}{dt}\{I_m\sin(\omega t-\theta)\}+\frac{1}{C}\int I_m\sin(\omega t-\theta)dt\hspace{15pt}(3)$$ Here, there are two options: to …

Considering the RL series circuit shown in Figure 1, and assuming that the DC power supply is E and the current that flows through the circuit after t seconds is I, the following formula holds true. $$E=RI+L\frac{dI}{dt}\hspace{50pt}(1)$$ Let’s consider how to solve a differential equation using the Laplace transform to find the current I. Laplace …

fig.1 RL series circuit(Alternating current) Now, let’s consider an RL series circuit as shown in Figure 1, assume the AC power source is E, and think about how to find the current I that flows t seconds after turning on the switch. Now, in the circuit of Figure 1, the following circuit equation holds true …