A coil of resistance `100Omega`, an inductor of 0.5 H and a capacitor of `15muF` are connected in series with a `200V-50Hz` AC source. Calculate the current in the circuit.

Explanation

Given : `R=100Omega,L=0.5H,C=15muF=15xx10^(-6)F,V_(rms)=200V,f=50Hz`
Induced reactance is given by,
`X_(C)=(1)/(Comega)=(1)/(2pifC)=(1)/(2xx3.14xx50xx15xx10^(-6))=212.2Omega`
`X_(L)=Lomega=2pifL=2xx3.14xx50xx0.5`
`X_(L)=157.1Omega`
Impedance of a series LCR circuit is given by,
`Z=sqrt(R^(2)+(X_(L)-X_(C))^(2))=sqrt((100)^(2)+(157.1-212.1)^(2))=114.1Omega`
Current through the circuit is given by,
`i_(rms)=(v_(rms))/(Z)=(100)/(114.1)=1.752A`