Question

An RLC series circuit has a 1.06 kN resistor, a 165 pH inductor, and a 21.0 nF capacitor. (a) Find the power factor at f = 7.50 kHz. (b) What is the phase angle (in degrees) at this frequency? (c) If the voltage source has Vrms = 408 V, what is the average power (in W) at this frequency? (d) Find the average power (in W) at the circuit's resonant frequency.

Answer 1

a)

tan x = ( 2 pi f L - 1/ ( 2 pi f C)) /R

tan x = ( 2* 3.14* 7500* 165* 10^-6 - 1 / ( 2* 3.14* 7500* 21* 10^-9))/ 1060

tan x = - 0.9465

x = - 43.42

power factor

cos x = 0.7263

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b)

x = - 43.42

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c)

impedance of circuit

Z^2 = 1060^2 + ( 2* 3.14* 7500* 165* 10^-6 - 1 / ( 2* 3.14* 7500* 21* 10^-9))^2

Z = 1459.49 ohm

P = Vrms^2 / Z cos x

P = 82.843 W

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d)

P' = Vrms^2 / R

P' = 157.04 W