A capacitor of unknown capacitance, a resistance of 100 ohm and an inductor of inductance `L = 4//pi^(2)` henry are connected in series across an a.c. source of 200 V, 50 Hz. Calculate the value of capacitance and the current that flows in the circuit, when the current is in phase with the voltage.

Explanation

Here, `R = 100 Omega, L = (4)/(pi^(2)) H`,
`E_(v) = 200 V, v = 50 Hz, C = ?, I_(v) = ?`
As current in phase with voltage, therefore,
`X_(C ) = X_(L) , (1)/(omega C) = omega L`,
`C = (1)/(omega^(2) L) = (1)/((2 pi v)^(2) L)`
`C = (1)/(4 pi^(2) v^(2) L) = (1 xx pi^(2))/(4 xx pi^(2) xx 50^(2) xx 4)`
`= 25 xx 10^(-6) F = 25 mu F`
As `X_(C ) = X_(L)`,
`:. Z = R = 100 Omega`
`I_(v) = (E_(v))/(Z) = (200)/(100) = 2 A`