Question

A resistor of 50 ohm, an inductor of `(20//pi)` H and a capacitor of `(5//pi) mu F` are connected in series to an a.c. source 230 V, 50 Hz. Find the current in the circuit.

Answer 1

Here, `R = 50 ohm`
`L = (20)/(pi) H, C = (5)/(pi) mu F = (5xx 10^(-6))/(pi) F`
`E_(v) = 230 V, v = 50 Hz, I_(v) = ?`
`X_(L) = omega L = 2 pi v L = 2 pi v ((20)/(pi))`
` = 40 xx 50 = 2000 Omega`
`X_(C ) = (1)/(omega C) = (1)/(2 pi v c) = (1 pi)/(2 pi v xx 5 xx 10^(-6))`
`= (1)/(10 xx 50) = 2000 Omega`
` Z = sqrt(R^(2) + (X_(L) - X_(C ))^(2))`
`= sqrt(50^(2) + (2000 - 2000)^(2)) = 50 Omega`
`I_(v) = (E_(v))/(Z) = (230)/(50) = 4.6 A`