Question

Consider the following circuit involving a 2F capacitor connected to resistors and a voltage source.

(e) (5 points) Determine the mathematical expression for UL (10 points) Consider the following circuit involving a 2F capacitor connected to resistors and a voltage source. Given that vc(0) = 2V, find the voltage of the capacitor as a function of time for t > 0 692 232 10V 332 2F+ VC Figure 2: (a) (5 points) Find the Thevenin equivalent circuit with Thevenin voltage and Thevenin resistance. (Consider capacitor as a load node) (b) (5 points) What is vc(t)?

Answer 1

voltage across capacitor is not suddenly change . so voltage vc at time just before t=0 and just after t=0 is same   volatge across capacitor for t>0 is solved in question (b)  

-Uunjan Date Page - - - - - o C = 2V so (a) vello) - Vecot) = Velo = 2v bl a A. MAMA 3r 2 tve We have to A and B find So Thevenin equivalent open circuit the across Capacitor Lood. Tov. httOFT I 31 1 Vrh I Node A and B is open circuit So Current across ! 22 Resistence is zero. Dentro - Apply Kirchoff's Voltage law in Loop I 10 - 61 +31 9 Vin = Thevenin Voltage Apply Kirchoff's Voltage law in Loop I

V = 2x0 + 3 ITEN Vani's 3x10 War: $ I = ng Ama Uth - 10 voit Now we have to find Thevenin Resistance (Rah) across Capacitor Load Books Short circuit the voltage Source nu in A 33 coB "Rih B Rn 7 ir R, and R2 Resistances are in paralled T hen hea - R, R2 RRE Ree equivalent Resistance b ) ! J Ski Roth So Rith = (2+2) r = 40 Gros Thevenin eque equivalent circuit is Furah tef Ran=45 Vinalo volt MM Vnet

RAB - Resisrence Across Mode A and B CAB - Capacitance across Aand B Gunjan Date Page 1 (b) What is vect) for t>o. Volt) = final value + [initial value - final value Te 42 zo Time , Constant Time Constant for Rc circuit is Rea Cea A for Time Constant ZERAB CAB lo 4x2 2=8 Reg = Rqh = 45 Cegs 2F: ?.. mm A T: 4x2, més 4 R ob -AB Vilth - Ve 400) + [ Velo) - Vc cool] é Vc.CO) is at Steady State Capacitor Open Circuited. So in " Ouestion(a) we find Vollege - the load Capacitor when - is open circuited is van V.CO) = Von = 10 voit becomes previous across Capacitor Tove video R . Van= VABI

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GUN Gunjan for finding time constant we have short circuit volsage source as eve did in question @ TO find Thevenih equivalent Resisrance Ran and Date Load Capacitance so t= Ranc = 4x2=8 Apply KVL in Loop 28+ Page 10 = 61 +31 91 -10 I stop Van = 3 XI Nan = 3x10 Vin = vc COO) = lo volt. Velt) = Vc (00) + [velos a Ve cool 7e" Nect) = Vect) = Ve (t) = 10 + [2 = 10 7 et 18 10 1.330 3:33 -133e te

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