An inductor 20 mH, capacitor 100 μF and a resistor 50 Ω are connected in series across a source of emf, V= 10sin⁡(314t⁡). The power loss in the…

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An inductor 20 mH, capacitor 100 μF and a resistor 50 Ω are connected in series across a source of emf, V= 10sin⁡(314t⁡). The power loss in the circuit is

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Correct answer: (C) 0.79 W. V_0=10 V, ω=314 rad/s P=V_rmsI_rmscos⁡ϕ P=V_rms V_rms/Z R/Z =(( V rms )^2 R)/(Z^2) X_L=ωL=314 20×10^(-3)=6.280 X_C=1/(ωC)=1/(314×100×10^(-6))=31.84 Ω R=50 Ω Z=√(( X C − X L )^2 +R^2) = √(31.84-6.28^2+50^2)=56 Ω ⇒P=(( 10 2 )^2 × 50)/(( 56 )^2) =0.79 W

An inductor $20 mH,$ capacitor $100 μF$ and a resistor $50 Ω$ are connected in series across a source of emf, $V = 10 \sin (314 t)$ . The power loss in the circuit is

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