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Fig. shows series LCR circuit with L = 5...

Fig. shows series LCR circuit with `L = 5.0 H, C = 80 mu F, R = 40 Omega` connected to a variable frequency 240 V source. Calculate
(i) the angular freuquency of the source which drives the circuit at resonance.
(ii) Current at the resonanting frequency.
(iii) the rms pot. drop across the capacitor at resonance.

Text Solution

Verified by Experts

Here, `L = 5.0 H`,
`C = 80 mu F = 80 xx 10^(-6) F, R = 40 ohm`
`E_(v) = 240 V, omega = ?, I = ?, V_(C ) = ?`
At resonance, `X_(L) = X_(C )`
`omega = (1)/(omega C)` or `omega = (1)/(sqrt(LC))`
`omega = (1)/(sqrt(5.0 xx 80 xx 10^(-6))) = (1000)/(20) = 50 rad//s`
(ii) At resonance. `Z = R =40 Omega`
`I_(v) = (E_(v))/(Z) = (240)/(40) = 6 A`
(iii) `V_(C ) = I_(v) X_(C )`
`= (I_(v))/(omega C) = (6)/(50 xx 80 xx 10^(-6)) = (6000)/(4) = 1500 V`
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