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

`R=40Omega`
`L= 3 mH = 3 xx 10^(-3) H `
`C= 2 muF = 2 xx 10^(-6)F`
` E_v = 110 V`
`v=5000 Hz`
` Z= ?`
`I_v= ?`
`Z=sqrt(R^2+(X_L-X_C)^(2))=sqrt(R^2+(2pivL-1/(2pivC))^(2))`
`Z=sqrt((40)^2+[(2xx3.14 xx5000xx3xx10^(-3)-(1)/((2xx3.14xx5000xx2xx10^(-6))))]^(2))`
`=sqrt(1600+(30xx3.14-1000/(62.8))^(2))`
`=sqrt(1600+(94.2-15.92)^(2))=sqrt(1600+(78.28)^(2))`
`Z = sqrt(1600+6127.76)=sqrt(7727.76)`
`I_(rms)=I_v = E_v/Z`
`I_v = 110/(87.91)=1.25A`