Saved Bookmarks
| 1. |
A capacitor with capacitance C and a coil with active resistance R and inductance L are connected in parallel to a source of sinusoidal voltage of frequency omega. Find the phase difference between the current fed to the circuit and the source voltage. |
|
Answer» Solution :We use the METHOD of complex voltage `V=V_(0)e^(iomegat)` Then `I_(C)=(V_(0)e^(iomegat))/( (1)/( iomegaC))=iomegaCV_(0)e^(iomegat)` `I_(L,R)=(V_(0)e^(iomegat))/( R+iomegaL)` `I=I_(C)+I_(L,R)=V_(0)(R-iomegaL+i omegaC(R^(2)+omega^(2)L^(2)))/(R^(2)+omega^(2)L^(2))e^(iomegat)` Then taking the REAL part `I=(V_(0)sqrt(R^(2)+{omegaC(R^(2)+omega^(2)L^(2))-omegaL}^(2)))/(R^(2)+omega^(2)L^(2))cos(omegat-varphi)` where` TAN varphi=( omegaL-omegaC(R^(2)+omega^(2)L^(2)))/(R)` 
|
|