A Sinusoidal Voltage of Peak Value 283 V and Frequency 50 Hz is Applied to a Series LCR Circuit | Bzziii

A sinusoidal voltage of peak value 283 V and frequency 50 Hz is applied to a series LCR circuit in which R = 3 Ω, L = 25.48 mH, and C = 796 µF, then the power dissipated at the resonant condition will be- 

(i)39.70 kW 
(ii) 26.70 kW 
(iii)13.35 kW 
(iv)Zero 

(iii)13.35 kW 

Explanation:

A sinusoidal voltage of peak value 283 V and frequency 50 Hz is applied to a series LCR circuit in which R = 3 Ω, L = 25.48 mH, and C = 796 µF, then the power dissipated at the resonant condition will be 13.35 kW .

V。= 283 V,
f = 50 Hz
R = 3 Ω,
L = 25.48 mH
C = 796 μF P` |_{at resonance}` = ?

Power dissipated P = `"l"^{2}"R"`

l = `\frac{"l"_{"o"}}{\sqrt{2}}`=`\frac{1}{\sqrt{2}}(\frac{283}{3})`

= 66.7 A

P = `"l"^{2}"R"` = `(66.7)^{2}"3"` = 13.35 kW

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CBSE Class 12 Physics Sample Paper-2022