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A circuit containing a 0.1 H inductor an...

A circuit containing a `0.1 H` inductor and a `500 muF` capacitor in series is connected to a `230` volt `100//pi Hz` supply.The resistance of the circuit is negligible. (a)Obtain the current amplitude and `rms` values. (b)Obtain the `rms` values of potential drops across each element ( c)What is the average power transferred to the inductor?(d)What is the average power transferred to the capacitor?(e)What is the total average power absorbed by the circuit ?[Average implies average over one cycle]

Text Solution

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The correct Answer is:
(a)`23sqrt2 A,23A` , (b)`460` volt, `230` volt , (c )zero , (d)zero , (e)zero
Given that
`L=0.1 H`
`C=500xx10^(-6) F`
`V_(rms)=230` volt , `f=100/piHz`
(a)`I_(rms)=V_(rms)/Z=230/Z`
where `Z=omegaL-1/(omegac)=2pi f L-1/(2pi^(f)C)=20-10=10`
& `I_(@)=sqrt2xxI_(rms)=23sqrt2`
(b)`V_(L)=I_(rms)(omegaL)`
( c )`lt P_(L) gt=I_(rms)V_(rms)cos phi`
(d)`lt P_(C) gt=0`
(e)`lt P_("net") gt=0`
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