Question

A capacitor of capacitance `100 muF` and a coil of resistance `50 Omega` and inductance `0.5 H` are connected in series with `a 110 V, 50 Hz AC` source. Find the rms value of the current.

Answer 1

Here, `C = 100 mu F = 100 xx 10^(-6) F`
`= 10^(-4) F`
`R = 50 ohm, L = 0.5 H, E_(v) = 110 V, v = 50 Hz`.
`X_(L) = omega L = 2 pi v L = 2 xx 3.14 xx 50 xx 0.5 = 157 Omega`
`X_(C ) = (1)/(omega C) = (1)/(2 pi v C)`
`= (1)/(2 xx 3.14 xx 50 xx 10^(-4)) = 31.85 Omega`
`Z = sqrt(R^(2) (X_(L) - X_(C ))^(2))`
`Z = sqrt(50^(2) + (157 + 31.85)^(2)) = 134.77 ohm`
`I_(v) = (E_(v))/(Z) = (110)/(134.77) = 0.816 A`