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CBSE Class 12-science Answered

The figure shows a series LCR circuit with L= 5.0 H, C = 80 μF, R = 40Ω connected to variable frequency 240 V source. Calculate (i) The angular frequency of the source which driver the circuit at resonance. (ii) The current at the resonating frequency. (iii) The rms potential drop across the capacitor at resonance.
Asked by Topperlearning User | 22 Jun, 2015, 08:38: AM
answered-by-expert Expert Answer

L = 5.0

C = 80μF

R = 40Ω

ε = 240 v.

(i) ω = begin mathsize 12px style fraction numerator 1 over denominator square root of LC end fraction end style= angular frequency

        =begin mathsize 12px style fraction numerator 1 over denominator square root of 5 space straight x space 80 space straight x space 10 to the power of negative 6 end exponent end root end fraction end style

        =begin mathsize 11px style fraction numerator 1 over denominator square root of 4 space straight x space 10 to the power of negative 4 end exponent end root end fraction equals space fraction numerator 1 over denominator 2 space straight x space 10 to the power of negative 2 end exponent end fraction equals 100 over 2 equals 50 Hz. end style

(ii) The current at the resonating frequency.    

  I = Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '. = begin mathsize 12px style 240 over 40 end style

   therefore I at resanating frquency = 6 A

(iii) Vrms = Irms XC 

      XC = begin mathsize 11px style 1 over ωc equals fraction numerator 1 over denominator 50 space straight x space 80 space straight x space 10 to the power of negative 6 end exponent end fraction end style

    begin mathsize 11px style therefore space straight V subscript rms space equals space fraction numerator 6 over denominator 50 space straight x space 80 space straight x space 10 to the power of negative 6 end exponent end fraction equals space fraction numerator 6 over denominator 4000 space straight x space 10 to the power of negative 6 end exponent end fraction equals space fraction numerator 6 straight x space 10 cubed over denominator 42 end fraction end style= 142.86 V

Answered by | 22 Jun, 2015, 10:38: AM

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