Question

Please help me with the exercise 2:

Consider the circuit shown where L=5 H, C=10 uF, Vo=220. The switch is closed at t=0, determine the expression for the voltage across the capacitor. Sketch the voltage across the capacitor, inductor, and the diode. Sketch the current flowing through the circuit

Thanks :)

1. For the current waveform, determine the average, rms, and peak current ratings 2. Consider the circuit shown where L-5 H, C=10 uF, Vo=220V. The switch is closed at t=0, determine the expression for the voltage across the capacitor. Sketch the voltage across the capacitor, the inductor, and the diode. Sketch the current flowing through the circuit.

Answer 1

Let us Redraw the circuit for ease. ia Vo = *S*H 3 LVL Let vos instral capaertor voltage. Let us usume apply kirchoffs voltage low in the loop, and cefsume crude is on Twe-vo-V-01 - 0 :: [Ve= Non obe Il | Idt modelling initial capacitor. vo ( Vc I 1 >> Ves Vo-t [Iolt.

Substituting in equcetion , at -o- LdI to at [Assume Zerochrop across drode in On State) Vo = t d I + / Siat Applying Laplace Treine form, Laplace of differentration » I Laplace dI Ics) s Ics) E dt I Laplace of Integration - I y fiat Ics) It I dt Ics)

& Vorss=Ls Ies) + Ies) sc => Tess = se Vors) s²LC +1 since, No=220 uce) ; ue4l= unit step as I afterto, voltage is applied. Laplace of Voss Ves) - No = 220 s. > Ies) a sc Vo S?LCHI vo => I S2+1 & LC Laplace of (sinut ult)) 24 w2

> IN = Vo a ta XV c. " => Ics) = Vo ſe v Taking Inverse Laplace, ماه Iet) = Vor sin ( 1 ) . - 6 From the circuit we can see Ve = V = Ld I (t) = Lofert costat Ne = Vo cus ( 7 ) eft

from , putting values, Icta 220x 10x10 6 cinct 5x10x10 220XHorto Hoyto-6 Ha sin at 2) It=311.127x103 sin(141.42 A -> Ic+)=311.127 Sin (1411:42 €) umat Te = 220 Cos (141-42+) W At wt= ñ, I cf) = 0, at the same time, Ne = -220v, after a coment wave form tries to become negative, but, since diode doenot cellow reverse current, diode is reverse biased & hence, clrode stops concluction & since current is zero, Voltage across incluctor Ve=LdI = 0, but voltage. at

across the capa istor is still €220 volts, 8 the capacitor cannot discharge as the drode Stops conduction, hence, there is no the circuit will resume & orduction . The voltage acros cliode is, Ve-Vo - Vezo (attañ, ->-220 - VD-0-0 , => [Vo = -220v after tani Before tañ, drode was conducting so, Vo = 0; initially.

-31 1.12717 wt . - - - 220 Zo ... Lyut 220 -- +220 ut 2) - 220 Jo wt 220V - - -