Docstoc

Class 5 R-C Circuit

Document Sample
Class 5  R-C Circuit Powered By Docstoc
					      EC 101
Electrical Sciences


   Lecture 5
  CIRCUIT
 ANALYSIS
TECHNIQUES
     R-C Circuit

                   t=0



            +
V0         VC(t)               R
              -          C




        Find VC(t) for t > 0
For t < 0,

VC (t) = V0




                +
V0
              VC (t)   C
                 -


        t<0
       For t > 0              t>0

                        +

      Applying KCL,   VC(t)   C     R

                        -


or,

 Solution :
Ex : If the switch has been connected for a long time to ‘a’ before
connecting to ‘b’ at time t = 0, find v(t) and i(t) for the following
circuit.


                                      a
                                       b
t 0
t 0
       τ = ReqC

       C = 50mF

        Req = RTh = ?
    Req = RTh


                         60Ω   200Ω   50Ω
R eq  60 200 50  24Ω
t 0
t 0
          Vf




  Vf 50
    
  24 60
Vn(t) + Vf
Ex.2 In Fig.1 the switch was closed for a long time and
     it opens at t = 0. Find Vc(t) for t > 0.


            5Ω                          4Ω          t=0
                                  +
                                  VC
Vc /4   +          10Ω            1µF                     40V
        -                         -




                         Fig.1
Solution :

For t < 0 , the circuit looks ,

                                       Vc

                      5 ohm                        4 ohm



     +     VC
     -                        10 ohm        1 uF           40V
           4




         Using nodal analysis ,

         (VC – VC/4)/5 + VC/10 +(VC – 40) /4 = 0
  [No current through capacitor as capacitor is open circuit to D.C)
or , 3VC/20 + VC/10 + (VC – 40 )/4 = 0
       3VC + 2VC + 5VC – 200 = 0
               10VC = 200
           VC = 20V for t < 0.
 For t > 0 the circuit becomes ,

                                     Vc

                5 ohm

        +            10 ohm
 Vc/4                                     1 uF
        -
        -



VC (forced) will be 0 as there is no forcing function.
        VC(t) will be only natural response
         VC(t) = Ae-t/τ    where τ = ReqC
   To find Req , let us apply a test voltage Vtest ,
                                               itest

                   5 ohm

  Vtst/4 +                   10 ohm        Vtest
          -



Applying nodal analysis ,
(Vtest – (Vtest/4))/5 + Vtest/10 = itest
3Vtest/20 + Vtest/10 = itest
3Vtest + 2Vtest = 20itest
5Vtest = 20itest
Vtest/itest = 4
Req = Vtest/itest = 4ohm
τ = Req.C = 4 x 1 x 10-6 sec
                 t

VC t   Ae   410  6
                           Ae    25104 t



Now, VC (t =0-) = VC (t = 0+) = VC (t = 0) = 20V

 Putting this condition, we get, A = 20

  So,   for t > 0


   VC t   20e          25104 t

				
DOCUMENT INFO
Shared By:
Categories:
Stats:
views:17
posted:4/15/2010
language:English
pages:22