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A series AC circuit containing an induct...

A series AC circuit containing an inductor `(20 mH),` a capacitor (120 `mu F`) and a resistor (`60 Omega`) is driven by an Ac source of 24 V/50Hz. The energy dissipated in the circuit in 60 s is :

Text Solution

Verified by Experts

Given `R=60 Omega, f=50Hz, omega=2pif=100pi` and `v=24v`
`C=120muf=120xx10^(-6)f`
`x_(C)=1/(omega C)=1/(100pixx120xx10^(-6))=26.52Omega`
`x_(L)=omegaL=100pixx20xx10^(-3)=2piOmega`
`x_(C)=x_(L)=20.24~~20`

`z=sqrt(R^(2)+(x_(C)-x_(L))^(2))`
`z=20sqrt(10)Omega`
`cos phi=R/z=60/(20sqrt(10))=3/(sqrt(10))`
`P_(avg)=VIcos phi,I=v/z=(v^(2))/zcos phi=8.64` watt
Energy dissipatd (Q) in time t = 60s is
`Q=P.t=8.64xx60=5.17xx10^(2)J`
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