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Figure shows a series LCR cicuit connect...

Figure shows a series LCR cicuit connected to a variable voltage source `V=10sin(omegat+pi//4), x_(L)=10Omega, X_(c)=6Omega, R=3Omega`
Calculate `Z, i_(0), i_(rms), V_(rms), V_(LO), V_(CO), V_(RO), beta, V_(LRms), V_(CRms), V_(Rms), i(t), V_(L)(t), V_(e(t)), " and " V_(R(t))`

Text Solution

Verified by Experts

`V=10sin(omegat+pi//4) " so " V_(0)=10` volt
`V_(rms)=10/sqrt(2)` volt
`therefore Z=sqrt(R^(2)+(X_(L)-X_(C))^(2))=sqrt(9+16)=5`
`i_(0)=v_(0)/z=2`
`i_(rms)=sqrt(2)A`
`V_(LO)=i_(0)X_(L)=20" volt " , V_(CO)=i_(0)X_(L)=12` volt
`V_(RO)=i_(0)R=6` volt , `V_(LRms)=20/sqrt(2)` volt
`V_(CRms)=20/sqrt(2)"volt ", V_(RRms)=6/sqrt(2)` volt
`cosbeta=R/Z=3/5 rArr beta=53^(@)`
`i(t)=20sin(omegat+pi//4-53^(@))`
`V_(L)(t)=20sin(omegat+pi//4-53^(@)+pi//2)`
`=20sin(omegat+(3pi)/4-53^(@)-pi//2)`
`=12sin(omegat-pi/4-53^(@))`
`V_(R(t))=V_(RO)sin(omegat+pi/4-53^(@))`
`=6sin(omegat+pi/4-53^(@))`
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