if 3 tan theta = 4 , find the value of 4sin theta -3 cos theta / 2 sin theta + 6 cos theta
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Answer:
general a CPE cano not be replaced by a capacitor. A capacitor can be treated as a pure good capacitor connected in parallel to a high resistance. The impedance is Z*=Z'-j Z" , Z'=R/(1+(wRC)^2 ), Z"=wRC R/(1+(wRC)^2 ) = wRC Z'. So current flowing through such a circuit will be equal to v exp(jwt) / Z* = v exp(jwt)/ (Z'-jZ")
= [v exp(jwt) ] ( Z' +j Z")/ (Z' ^2 + Z" ^2) ) = [ v exp(jwt) ] exp (j theta ) with cos(theta)=( Z' )/ (Z' ^2 + Z" ^2) ) and
sin (theta) = ( Z")/ (Z' ^2 + Z" ^2) ) .THe phase angle is given by Tan(theta)=Z"/Z' = wRC. That means the phase angle is not a constant and is frequency dependent. In the same way you can show that no pure lumped elements or usual combinations of these gives a CPE. A Z" vs Z' plot for a CPE is a straight line ( frequency indepedndant). So where ever experiments show a straight line in immitance ( impedance, admittance, permittivity, modulus) a CPE is assumed to be present in the model equivalent circuit Afterwards various meanings are atrributed to the material. You can see some of our papers by searching at google with name L Pandey or Lakshman Pandey where we have tried to simulate these behaviours. I was using my own Complex Non Linear Least Sqares program that I wrote in BASIC in eraly 90's. If you feel interested pl let me know , I will dig out our papers and tell you.