A `40Omega` resistor, 3m H inductor and `2muF` capacitor are connected in series to 110V, 5000 Hz AC source.Calculate Impedenceof the circuit and value of current in the circuit.

Explanation

Non-inductive résistance `R= 50 Omega`
`L= 0.3 H`
` C = 40 muF = 40 xx 10^(-6)F`
`E_v= 200 V`
` v= 50 Hz`
Impedance = Z = ?
`I_v = ?`
`Z = sqrt(R^2+(X_L-X_C)^2)`
`Z = sqrt(R^2+(2pivL-1/(2pivC))^(2))`
`Z = sqrt(R^2+(2pivL-1/(2pivC))^(2))`
`=sqrt((50)^2+[(2xx3.14xx50xx0.3)-1/(2xx3.14xx50xx40xx10^(-6))]^(2))`
`Z = sqrt(2500+(94.2-(1000000)/(3.14xx40))^(2))`
`= sqrt(2500+(94.2-79.6)^(2))`
`=sqrt(2500+(14.6)^(2)) = sqrt(2500+213.16)`
`Z = 52.09Omega`
`I_v = E_v/Z`
`=200/(52.09)I_v=3.84A`