in an RLC circuit such as that of the figure assume that R-6.82 , L-60.3 mm, a-6

Question

in an RLC circuit such as that of the figure assume that R-6.82 , L-60.3 mm, a-60.0 Hz, and Em-22.5 V. For what values of the capacitance would the average ate at which energy is dissipated in the resistance be (a) a maximum and (b) a minimum angle and (e) power f 9 What are (e) the maximum dissipation rate and the corresponding (d) phase actor? What are (1) the minimum dissipation rate and the corresponding (o) phase angle and (h) power factor? (a) Number (b) Number (c) Number (d) Number (e) Number (t) Number

Explanation / Answer

R = 6.82 Ohm ; L = 60.3 mH ; em = 22.5 V ; f = 60 Hz

a)We know that Z is minimum when

Xl = Xc

2 pi f L = 1/ 2 pi f C

C = 1/4 pi^2 f^2 L

C = 1/[4 x 3.14^2 x 60^2 x (60.3 x 10^-3)^2] = 1.17 x 10^-4 F

Hence, C = 1.17 x 10^-4 F

b)For this C = 0F

c)P = Erms^2 R/Z^2 = em^2/2R = 22.5^2/2 x 6.82 = 1.65 W

Hence, P = 1.65 W

d)we know that

phi = tan^-1[(XL - Xc)/R] = 0

phi = 0 deg

e)Pf = cos(phi) = cos0 = 1

PF = 1

f)P = 0

Since, Xc = infinity

g)phi = tan^-1[(XL - Xc)/R] = tan^-1(-infinity) = -90

phi = -90

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