In an RLC circuit such as that of the figure below assume that R = 7.00 , L = 60

Question

In an RLC circuit such as that of the figure below assume that R = 7.00 , L = 60.0 mH, fd 60.0 Hz, and = 25.0 v. st (a) For what value of the capacitance would the average rate at which energy is dissipated in the resistance be a maximum? (b) For what value would it be a minimum? (c) What is the maximum energy dissipation rate? (d) What is the corresponding phase angle? (e) What is the corresponding power factor? (f) What is the minimum dissipation rate? (g) What is the corresponding phase angle? (h) What is the corresponding power factor?

Explanation / Answer

for the given RLC circuit

R = 7 ohm

L = 60 mH

fd = 60 Hz

Em = 25 V

a. energy dissipated in resistance is maximum for resonance

hence

C = 1/w ^2*L

and w = 2*pi*fd

hence

C = 1.172698*10^-4 F

b. energy dissipated in resistacne is minimum for Xr^2 = (Xc - Xl)^2

49 = (2*pi*fd*L - 1/2*pi*fd*C)^2

C = 1.69825*10^-4 F

c. Maximum energy dissipation rate = V^2/R = 89.285 W

d. corresponding phase angle = 0 deg

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