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Electric Charges And Fields

Question
CBSEENPH12039077

The figure shows a series LCR circuit with L = 5.0 H, C = 80 mF, R = 40 W connected to a variable frequency 240V source. Calculate. 


(i) The angular frequency of the source which drives the circuit at resonance.

(ii) The current at the resonating frequency.

(iii) The rms potential drop across the capacitor at resonance.

Solution

Given a series LCR circuit,

i) At resonance, angular frequency is given by, 
        bold italic omega subscript bold italic r space equals space fraction numerator 1 over denominator square root of bold italic L bold italic C end root end fraction equals fraction numerator 1 over denominator square root of 5 cross times 80 cross times 10 to the power of negative 6 end exponent end root end fraction

space space space space space equals space 50 space rad divided by sec
ii) Current at resonating frequency is given by, 
        straight I subscript rms straight space equals straight space straight V subscript rms over straight R equals straight space 240 over 40 equals straight space 6 straight space straight A
iii) RMS potential drop across the capacitor at resonance is given by, 
V subscript r m s end subscript italic space equals I subscript r m s end subscript cross times space chi subscript c

italic space italic space italic space italic space italic space italic space italic space equals space 6 cross times fraction numerator italic 1 over denominator italic 50 italic cross times italic 80 italic cross times italic 10 to the power of italic minus italic 6 end exponent end fraction

space space space space space space space equals space fraction numerator 6 cross times 10 to the power of 6 over denominator 4 cross times 10 cubed end fraction italic space

space space space space space space space equals space 1500 space straight V