Please answer all parts of the question. In an RLC circuit such as that of the f

Question

Please answer all parts of the question.

In an RLC circuit such as that of the figure assume that R = 5.58 Ohm, L = 55.0 mH, f_d = 72.0 Hz, and epsilon_m = 40.1 V. For what values of the capacitance would the average rate at which energy is dissplated in the resistance be (a) a maximum and (b) a minimum? What are (c) the maximum dissipation rate arid the corresponding (d) phase angle and (c) power factor? What are (f) the minimum dissipation rate and the corresponding (g) phase angle and (h) power factor? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units (f) Number Units (g) Number Units (h) Number Units

Explanation / Answer

Avg Power is given by:

Pav = e^2 R/ Z^2

P will be max when Z is min and vice-versa.

a)Z will be min 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 72^2 x 55 x 10^-3) = 8.8 x 10^-5 F

Hence, C = 88 x 10^-6 F = 88 micro Farads

b)P is min when Z is maximum, Z is given by

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

clearly, Z will have its max value when Xc = 0 that 1/2 pi f C = 0 => C = 0.

Hence, C = 0

c)P = Erms^2 R/ Z = (Em^2/2) R/R^2 = Em/2R

P = 40.1^2/2 x 5.58 = 144.1 W

Hence, P = 144.1 W

d)we know that

phi = tan -1 (Xl - Xc)/R

Xl - Xc = 0 => phi = 0

Hence, phi = 0 deg

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