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A capacitor of capacitance C is connected in parallel with a choke coil having inductance I and resistancev R Calculate (a) The resonance frequency and (b) the circuit impedance at resonance . |
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Answer» SOLUTION :Impedance of `R -L` circuit `Z sqrt((R^(2)) + X_(L)^(2)` Voltage leads the current by phi where `tan phi = X_(L)/R` `i_(1) = (V)/(Z) = (V)/(sqrtR^(2) + X_(L)^(2))` `i_(2) = (V)/(X_(C))` At resonance voltage and current are in same phase for it `i_(2) =i_(1) SIN phi implies (V)/(X_(C)) =(V)/(sqrt(R^(2) + X_(1)^(2))) . (X_(L))/(sqrt(R^(2) + X_(1)^(2)))` `R^(2) + X_(L)^(2) = X_(L) X_(C) implies R_(2) + omega^(2) L^(2) =(L)/(C)` `omega = omega_(r) = sqrt((1)/(LC) - R^(2)/(L^(2)))` At resonance current `i = i_(1) cos phi` `(V)/(Z) = (V)/(Sqrt( R^(2) +X_(L)^(2))) .(R)/(sqrt(R^(2) + X_(L)^(2))) implies (1)/(Z) = (R)/(L//C)` Impedance at resonance `Z = (L)/(CR)`   .
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