In the series LCR circuit shown the impedance is

Options

A. `200 Omega`
B. `100 Omega`
C. `300 Omega`
D. `500 Omega`

Answer

D

Explanation

Here, `L = 1 H, C = 20 mu F = 20xx10^(-6)F`
`R=300 Omega, upsilon = (50)/(pi)Hz`
The inductivereactance is
`X_(L)=2pi upsilon L=2xxpixx(50)/(pi)xx1=100 Omega`
The capacitive reactance is
`X_(C )=(1)/(2pi upsilon C)=(1)/(2xxpixx(50)/(pi)xx20xx10^(-6))=500 Omega`
The impedance of the series LCRcircuit is
`Z = sqrt(R^(2)+(X_(C )-X_(L))^(2))=sqrt((300)^(2)+(500-100)^(2))`
`=sqrt((300)^(2)+(400)^(2))=500 Omega`