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A sinusoidal voltage of peak value 285 V...

A sinusoidal voltage of peak value 285 V is applied to a series LCR circuit in which resistor of resistance 5 W, pure Inductor of Inductance 28.5 mH and capacitor of capacitance 800 `mu` R are connected.
Calculate the impedance, current and power dissipated at the resonance.

Text Solution

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Given `V_(0)=285V,R=5W,L=28.5xx10^(-3)H,`
`C=800xx10^(-6)F.`
At resonance `X_(L)=X_(C)` and impedance Z = R.
Hence impedance `=5W,I=(V)/(Z)`
i.e, Current `I_("peak")=(V_("peak"))/(5)=(285)/(5)=57A.`
Power dissipated `(V_(p)I_(p))/(2)cosphi`
Where `f=0^(@)&cosf=cos0^(@)=1" at resonance "`
Power dissipated `=(285xx57)/(2)=812.W`
= 8.123 kW (kilowatt)
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