Question

17.6 Derive the relationship between the output, the potential difference across the resistor R of vx, and the input v for the series LCR circuit shown in Figure 17.23.

Answer 1

Given data Resistor is R, potential difference is VR input voltage is vi Consider the Circuit as shown below p uf Capacitor voltag Ve=- Q (..Q= charges differentiate above url. t.

dvc 1 da ! II dt Curent) duc CIH ОТ НА - Idt Idt Toe - Simila, ey the inductor voltage V = L di dt Similarly for U resistor voltage Vo = IR Apply kirchaft voktage above circuit v=vet et UR

V= ve tutur put the vola in above expression v= Ta Idt . - + L dI + IR че - те - Tolat The from above expression! 1 dt + d up tur R at RTR differentiate the both above equation l . Now side & w.r. On deur & 아 durt ot? dt

So, ordinary differential gration I d² wat att & up t dt I UR = RC ? du Whore ur input voltage U output voltage APRey th la place frous form on both side. 15² Up (s) + Suals) & Je(s) P. - su(s) UR(s) / Str + st 1 1 I È RC s Ves). - 5 UR(S) VC) vo - SCR s²ict Sretl