Question

8. 0/4 points s Answers SerPSE10 32.6 OP018 In a certain series RLC circuit, Irms-9.00 A, ΔΙ,ms-230 V, and the current leads the voltage by 33.0。 (a) What is the total resistance in te circuit? e axima of the current and voltage do not occur at the same time, so the current is not simply Ω (b) Calculate the reactance (in) of the circuit (XL- Xc). What If? If the voltage in the circuit is maintained by an AC source operating at f = 60.0 Hz and the resonant frequency of the circuit is f0 = 75.0 Hz, what are the values of C (in μF) and L (in mH) in the circ. mH Need Help?

Answer 1

Given v_RMS = 230v I_RMS = 9A current leads voltage by 33 degree therefore phase representation of I = 9 < 33 degree v = 230 < 0 therefore z_eq = v/I = 230 < 0/9 < 33 therefore z_eq = 25.5555 < - 33 degree ohm writing z_eq in Cartesian form z_eq = 21.4327 - j13.9185 Ohm Above values are found by using the relation squareroot R^2 + x_eq^2 = 25.5555 tan^-1 x_eq/R = ore x_eq = -13.9185 ohm-(1) Resonant frequency = 75Hz from eq(1) x_L = x_eq + x_c therefore x_L = -13.9185 + x_c-(2) x_L = -13.9185 + x_c x_L = -25 fL & x_c = 1/25fC operating frequency = 60Hz therefore x_L = 377L & x_c = 1/377c therefore 377L = -13.9185 + 1/377c 142129LC = -5247.2745c + 1 therefore c[142129L + 5247.2745] = 1 therefore c = 1 - 33 degree therefore value of Resistance = 21.4317 ohm b)Value of equivalent Reactance (x_L - x_c) x_L - x_c = x_eq theref /142129L + 5247.2745 Now resonant frequency occurs when x_L = x_c

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