Draw an RLC circuit with resistor (R=425 Ohms), inductor (L=1.25 H) and capacito

Question

Draw an RLC circuit with resistor (R=425 Ohms), inductor (L=1.25 H) and capacitor (C=3.50*10^-6 F) in
series with the AC power supply.

b)Find the maximum current in the circuit c)Calculate the phase angle if the frequency of the source is 60 Hz d)Determine the resonant frequency. e)Determine the quality factor. Using the equation blew,determine the value of gain on the resistor for frequency of the AC current approaching zero and approaching infinity. Justify your approximations (limits, simplifications). Gain -

Explanation / Answer

Given,

R = 425 ohm ; L = 1.25 H ; C = 3.5 x 10^-6 ; f = 60 Hz

a)Inductive reactance

XL = 2 pi f L

XL = 2 x 3.14 x 60 x 1.25 = 471 Ohm

Capacitive reactnace

Xc = 1/(2 x 3.14 x 60 x 3.5 x 10^-6) = 758.27 Ohm

Z = sqrt (R^2 + (XL - Xc)^2)

Z = sqrt (425^2 + (471 - 758.27)^2) = 513 Ohm

Hence, Z = 513 Ohm

b)Imax = Vmax/Z

Imax = Vmax/513 Ohm

[this part need input voltage]

c)phi = tan^-1 [(XL - Xc)/R]

phi = tan^-1 (471 - 758.27/425) = -34.1 deg

phi = -34.1 deg

d)At resonance

Xl = Xc

2 pi f L = 1/(2 pi f C)

f = 1/2 pi sqrt (LC) = 1/[2 x 3.14 sqrt(1.25 x 3.5 x 10^-6)] = 76.1 Hz

Hence, f = 76.1 Hz

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