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Give the expression for the impedance of an LCR circuit and obtain the expression for the resonant frequency. What is the power factor of the resonant circuit? |
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Answer» Solution :Impedance of a series LCR circuit is given by `Z=sqrt(R^(2)+(X_(L)-X_(C))^(2))=sqrt(R^(2)+(omegaL-(1)/(omegaC))^(2))` Where, `omega=2pif`, f being frequency of ac. i.e., `omega_(0)^(2)LC=1` `therefore omega_(0)=(1)/(sqrt(LC))or2pif_(0)=(1)/(sqrt(LC))` `therefore f_(0)=(1)/(2pisqrt(LC))`, where `f_(0)` is known as the resonant frequency. Power FACTOR = cos R/Z and Z = R at resonant frequency. Power factor = cos R/R = 1. VOLTAGE is in PHASE with CURRENT. |
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