Consider the parallel resonant circuit shown in adjacent figure. One branch contains an inductor of inductance L and a small ohmic resistance R, whereas the other branch contains a capacitor of capacitance C. The circuit is fed by a source of alternating emfE= E_(o) e^(jomegat)=E_(o)sin omegatThe impedance of inductor branch, Z (1)= R + jomegaL The impendence of capacitor branch, Z(2) = (1//jomegaC) therefour Net impedance Z of the two parallel branches is given by(1)/(Z)=(1)/(Z_(1))+ (1)/)Z_(2)=(1)/(R+jomegaC=(R-jomegaL)/(jomegaL)(R-jomegaL)+jomegaC=(R)/(R^(2)+omega^(2)+L^(2))+jomega[C-(L)/(R^(2)+omegaL^(2))]The current flowing in the circuitI=(E)/(Z)=(E)[(R)/(R^(2)+omega^(2)L^(2))+jomega(C-(L)/(R^(2)+omega^(2)L^(2)))]For resonance to occur, the current must be in phase with the applied emf. For this, the reactive component of current should be zero, l.e.omega[C-(L)/(R^(2)+omega^(2)L^(2))]=0orC=(L)/(R^(2)+omega_(r)^(2)L^(2))(writing omega_(r)for omegaat resonance) This gives resonant angular frequencyomega_(r)=sqrt((1)/(LC)-R^(2)/(L^(2))) At parallel circuit resonance, theimpendence is maximum and current is minimum. Parallel resonant circuit is sometimes called the anti-resonance in order to distinguish from series resonanceQFind the impedance of AC circuit at resonance shown in the adjacent figure For an ac circuit, impendence is given by Z = 50 + jK(P^(2) - 4Q^(2), where K is a positive non-. zero constant. For resonance, which of the following expression is true