1.

A sinusoidal voltage of peak value 293 V and frequency 50 Hz is applie to a series LCR circuit in which `R=6 Omega, L=25 mH` and `C=750mu F`. The impedance of the circuit isA. `7.0 Omega`B. `8.9 Omega`C. `9.9 Omega`D. `10.0 Omega`

Answer» Correct Answer - A
Here, `R = 6 Omega, L=25 mH=25xx10^(-3)H`,
`C=750 mu F = 750xx10^(-6)F, upsilon = 50 Hz`
`X_(L)=2pi upsilon L =2xx3.14xx50xx25xx10^(-3)=7.85 Omega`
`X_(C )=(1)/(2pi upsilon C)=(1)/(2xx3.14xx50xx750xx10^(-6))=4.25 Omega`
`therefore X_(L)-X_(C )=7.85-4.25=3.6Omega`
Impedence of the series LCR circuit is
`Z=sqrt(R^(2)+(X_(L)-X_(C ))^(2))`
`therefore Z=sqrt((6)^(2)+(3.6)^(2))=sqrt(36+12.96)=7.0 Omega`


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