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Fig. show a series LCR circuit with `L = 0.1 H l, X_(C ) = 14 Omega` and `R = 12 Omega` connected to a 50 Hz, 200 V source. Calculate (i) current in the circuit and (ii) phase angle between current and voltage. Take `pi = 3` |
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Answer» Here, `R = 12 Omega, X_(C ) = 14 Omega, L = 0.1 H` `E_(v) = 200 V, v = 50 Hz` `X_(L) = omega L = 2 pi v L = 2 xx 3 xx 50 xx 0.1 = 30 Omega` `Z = sqrt(R^(2) + (X_(L) - X_(C))^(2)) = sqrt(12^(2) + (30 - 14)^(2)) = 20 Omega` `I_(v) = (E_(v))/(Z) = (200)/(20) = 10 A` As `X_(L) gt X_(C )`, current lags behind the applied voltage by phase angle `phi`, where `tan phi = (X_(L) = X_(C ))/(R ) = (30 - 14)/(12) = 1.3333` `phi = tan^(-1) (1.3333) = 53.1^(@)` |
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