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An LCR circuit consists of L = 230 mH, C...

An LCR circuit consists of L = 230 mH, `C = 70 mu F` and `R = 200 Omega ` . The frequency of AC main is 60Hz and E = 36V . Calculate impedance Z, current I and angle `phi` .

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`X_C = (1)/(2pi v C) = (1)/(2 xx 3.14 xx 60 xx 70 xx 10^(-6) ) = 38 Omega`
` X_L = 2pi v L = 2 xx 3.14 xx 60 xx 230 xx 10^(-3) = 87 Omega`
`R = 200 Omega`
` Z = sqrt(R^2 + (X_L - X_C)^2) = sqrt(200^2 + (87 -38)^2)`
` = sqrt(200^2 + 49^2) = 206 Omega `
Current `I = E/Z = 36/206 = 0.174 A`
Phase `phi = tan^(-1) ( (X_L - X_C)/(R ) ) = tan^(-1) [ (87-38)/(200) ]`
`phi = tan^(-1) (0.245) = 13.8^@ = 13^@46.`
` V_R = IR= 0.174 xx 200 = 34.8 V`
` V_L = IX_L = 0.174 xx 87 = 15.1 V`
` V_C = IX_C = 0.174 xx 38 = 6.6 V `
`X_L gt X_C` so emf lead the current I.
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