mathematics electrical engineering

Calculation of RLC series circuit using complex numbers

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 …

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