NEED HELP WITH D-G (a) If an RCL series circuit contains a resistance R = 258 W,

Question

NEED HELP WITH D-G

(a) If an RCL series circuit contains a resistance R = 258 W, a capacitance C = 3.5 µF, and an inductance of L = 0.19 H, calculate the inductive reactance XL if the circuit is connected to a voltage source whose frequency is 357 Hz.

XL =  W     

(b) Calculate the capacitive reactance XC for the same conditions in part A.

XC = W     

(c) Calculate the impedance Z of the circuit at this frequency.

Z = W     

(d) If the rms voltage across the generator is 143 V, calculate the average power P(at 357 Hz) being used by the circuit.

P(at 357 Hz) =  W     

(e) Calculate the resonant frequency fres of the circuit using the above values for R, L, and C.

fres = Hz     

(f) Calculate the impedance Zres of the circuit at resonance.

Zres =  W     

(g) If the rms voltage across the generator is 143 V when at resonance, calculate the average power Pres being used by the circuit.

Pres =  W

Explanation / Answer

a)

XL = 2*f*L = 2*258*0.19 = 307.84

b) XC = 1/(2*f*C) = 1/(2*258*3.5 x 10^-6) = 176.34

c) Z = sqrt(R^2 + (XL - XC)^2) = sqrt(258^2 + (307.84 - 176.34)^2) = 289.58

d) P = V^2/Z = 143^2/289.58 = 70.62W

e) resonant f occurs when XL = XC or 2*f*L = 1/(2*f*C)

so f = (1/2)sqrt(1/LC) = (1/2)*sqrt(1/(0.19*3.5 x 10^-6) = 195.26 Hz

f) At resonance Z = R = 258

g) P = V^2/Z = 143^2/258 = 79.25W

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