(a) To find the impedance of the circuit, we first calculate `x_(L)` and `X_(C)`.
`x_(L)=2pivL`
`=2xx3.14xx50xx25.48xx10^(-3)Omega=8Omega`
`x_(c)=(1)/(2pivC)`
`=(1)/(2xx3.14xx50xx796xx10^(-6))=4Omega`
Therefore,
`Z=sqrt(R^(2)+(X_(L)-X_(C))^(2))=sqrt(3^(2)+(8-4)^(2))`
(b) Phase difference, `phi=tan^(-1)(X_(C)-X_(L))/(R)`
`=tan^(-1)((4-8)/(3))=-53.1^(@)`
Sinc `phi` is negative, the current in the circuit lags the across the source.
(c) The power dissipated in the circuit is
`P=I^(2)R`
Now, `l=(t_(m))/sqrt(2)=(1)/sqrt(2)((283)/(5))=40A`
Therefore, `P=(40A)^(2)xx3Omega=4800W`
(d) Power factor `=cosphi=cos(-53.1^(@))=0.6`