A series RLC circuit has a resonant frequency of 6.40 kHz. When it is driven at

Question

A series RLC circuit has a resonant frequency of 6.40 kHz. When it is driven at 8.00 kHz, it has an impedance of 1.15 kand a phase constant of 45

Explanation / Answer

a)w = sqrt(1/LC) = (2*(22/7)*6.4*(1000)) =>LC = 1/((2*(22/7)*6.4*(1000))^2) = 6.17918E-10 R^2 + X^2 = (1.15*1000)^2 and X/R = 1 =>X = R =>2R^2 = ((1.15*1000)^2) =>R = sqrt(((1.15*1000)^2)/2) = 813.1728 Ohms = 0.8131728 KOhms b)X = 813.1728 =>wL-1/wC = 813.1728 =>(2*(22/7)*8000)L-(1/(2*(22/7)*8000))*(1/6.17918E-10)*L = 813.1728 =>L = 0.044919583 H = 44.919583 mH c)C = 6.17918E-10/L = 1.37561E-08 F = 13.7561 nF

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