1.

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

Answer»

1.13 W
0.79 W
2.74 W
0.43 W

Solution :By COMPARING V=10 sin 314 t with equation
V=Vm sin Wt
Vm=10 V, W=314 rad `s^(-1) , L=20xx10^(-3)`H,
`C=100xx10^(-6) F , R=50Omega`
`X_L=WL=314xx20xx10^(-3)=6.28 Omega`
`X_C=1/(WC) =1/(314xx10^(-4))=31.85 Omega`
`THEREFORE |z|=sqrt(R^2+(X_L-X_C)^2)`
`=sqrt((50)^2+(6.28-31.85)^2)`
`=sqrt(2500+(25.57)^2)`
`=sqrt(2500+653.82)`
`=sqrt3153.82`
`therefore` |z|=56.16 `Omega`
Now, Power `P=I_m I_(rm) cos theta`
`=V_m/sqrt2xxV_m/(sqrt2xxZ)xxR/Z`
`=(V_m^2R)/(2Z^2)`
`=((10)^2xx50)/(2xx(56.16)^2)`
= 0.79265 W
`therefore P approx` 0.79 W


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