An 8 H inductor, a 2 `mu`F capacitor and a 100 `Omega` resistor are connected in series to an A.C. supply of 220 V and 50 Hz. Calculate :
(i) Impedance of the circuit.
(ii) Current flowing through the circuit.
(iii)Phase difference between the current and the supply voltage.
(iv) Average power consumed by the circuit.

Explanation

Given L = 8H , C = `2mu F, R= 100 Omega , f= 50 Hz, V= 220`V
`X_(L)= omegaL= 2pi fL`
`= 2pi 50 xx8`
= `2513 Omega= 25.13 k Omega`
`X_(c)= (1)/(omegaC) = (1)/(2pifC)`
`= (1)/(2pi 50 xx2xx10^(-6))`
`X_(c)= 15.92 k Omega= 16k Omega`
(i) `Z= sqrt(R^(2)+(X_(L)-X_(c))^(2))`
`Z= sqrt((100)^(2)+(2513-1592)^(2))`
Z=926.41 `Omega`
(ii) `I= (V)/(Z)`
`I= (220)/(926)= 0.2376 A `
(iii) `tan phi= (X_(L)-X_(c))/(R)`
` tan phi = (921)/(100)`
`phi= tan^(-1) (9.2)`
`phi =83.8^(@)`
(iv) Total power `= VxxI`
P = 220 V `xx 0.238 A ` = 52.36 Watts