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Following figure 6 shows a series RCL ci...

Following figure 6 shows a series RCL circuit connected to an ac source which generates an alternating emf of frequency 50 Hz. The readings of the voltmeters `V_(1)` and `V_(2)` are 80 V and 60 V respectively.

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

Text Solution

Verified by Experts

f=50 Hz
I=?
`V=IR_(1)`
`80=Ixx100`
`I=(80)/(100)=0.8A`
`V_(2)=60V`
`V_(2)=IxxX_(C)`
`60=0.8xxX_(C)`
`X_(C)=(60xx10)/(8)`
`=75Omega`
`X_(C)=(1)/(2pifC)`
or `C=(1)/(2pifxxX_(C))`
`=(1)/(2pixx50xx75)`
`=4.25xx10^(-5)F`
At resonance, Z=R as `X_(L)=X_(C)`.
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