Following figure shows a series RCL circuit connected to an a.c. source which generates an alternating emf of frequency 50 Hz. The reading of the voltmeter `V_(1)andV_(2)` are 80 V and 60 V respectively.

Find :
(1) the current in the circuit.
(2) the capacitance C of the capacitor.
(ii) At resonance, what is the relation between impedance of a series LCR circuit and its resistance R?

Explanation

(1) `f=50Hz`
`I=?`
`V=IR`
`80=Ixx100`
`I=(80)/(100)=0.8` amp.
(2) `V_(2)=60V`
`V_(C)=IxxX_(C)`
`60=0.8xxX_(C)`
`X_(C)=(60xx10)/(8)=75Omega`
`X_(C)=(1)/(2pifC)`
`C=(1)/(2pifxxX_(C))`
`=(1)/(2pixx50xx75)`
`=4.25xx10^(-5)F`