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A sinusoidal voltage of peak value 285 V is applied to a series LCR circuit in which resistor of resistance 5 W, pure Inductor of Inductance 28.5 mH and capacitor of capacitance 800 mu R are connected. Find the resonant frequency. |
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Answer» Solution :Given `V_("rms")= 285 V , R =5 Omega,L =28.5 mH=28.5xx10^(-3)H,C= 800mu F= 800xx10^(-6)`F a. Resonant FREQUENCY `gamma_(0)=(1)/(2pisqrt(LC))=(1)/(2xx3.14sqrt(28.5xx10^(-3)xx800xx10^(-6)))` `gamma_(0)=(1)/(2xx3.14sqrt(2.85xx10^(-2)xx800xx10^(-6)))=(1)/(6.28sqrt(2280xx10^(-6)))=(1)/(6.28xx47.74xx10^(-4))` `=(1)/(6.28xx47.74xx10^(-4))=(1)/(299.80xx10^(-4))=0.003335xx10^(4)=33.35` Hz b. Impedance , Z`= SQRT(R^(2)+(X_(L)-X_(e))^(2))` At resonance `X_(L) =X_(c)` `z=sqrt((5)^(2))` `Z= sqrt(25)` `Z = 5 Omega` `I_(rms) = (V_(rms))/(Z)= (285)/(5)` `I_(rms)= 57 A` Power dissipated at resonace `P=V_(rms)I_(rms)= 285xx57` `P = 16.245` watt |
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