Question

For the circuit shown below, find the equation for Vc(t) for t > 0

Draw the following circuits:

T =0

T = 0+

R_th

1. For the circuit shown in Figure 1 below, find the equation for vc(t) fort>0. Extra Credit: Find the time constant (T) and indicate how long it will take to fully discharge the capacitor voltage. Hint: You have to draw the following circuits at: t=0-, t=0+, RTH too 2 + W 3r - Velt) 24 9A - 5F Figure 1.

Answer 1

2 Vc (0) = 18 volt NcO) = VicoJ = Vc (ot) G Equal voltage due to steady Ostate position. *at to position of switch, circuit become 22 22 w + t. 42 sk 4.2 Vco) 75F Vccot] ligo tot circuit of tzo position and t= of i's Ciowit. We have to find Rth across Vc (t) tominals. and Cirmit become Same to M Roth =bah Rth Capacitor [ci= 5f Time constant of Rc croswit is of Re crow it is given by an formula Reqxc •T T = 6 x 5 e = 30 sec 30 sec -Time constant -t/e Vc ct] =vo e an formula from Re cirun't No Voltage arooss Copacitor af to le Ve OJ = 18 volto Vect)=18 el -+30 Ans. . Vcct) = 18 e volt. t

9.13 i) croant at at to 22 t=0 + 32 Vect) DA SF 4--2 at t= 0 Capacitor is at Slendy position and it has value constant & it act open ckt- & Vcco-) = Vcco) = Vcot) tao 2-2 Iz 11 t 9A 42 VC(0) I bi2.0 t= ó crow't 67. © He have to colculofe Vco) =? Current flowing 2 f4 e Resistor is calculated by using arrant division safe. flowing through in 3 A Iz 3 x9 376 6 I = X 9 - 64 376 Vc (0) = 3 X I 306 = 18 volt

• #Time Constantin It is the time taken by the response to reach 36.7% of its initial volve while dischargthing decaying OR It is a time taken by the Rosponse to reach 63.2% of its final or state value while steady charging

Time constant 30 sec.is required to discharge capacitor to its 36.7% of its initial value