A damped LC circuit loses 6.7% of its elextromagnetic energy per cycle due to thermal energy....

Question

Question

A damped LC circuit loses 6.7% of its elextromagnetic energy per cycle due to thermal energy. If L=85 mH and C=7.70 uF what is the value of R?

Answer 1

Answer #1

Angular frequency Wo = W' = 1/sqrt(LC)

W' = Wo = 1/(sqrt(0.085* 7.7*10^-6)

W0 = W' = 1236 rad/s

as W = 2pi f = 2pi/T

T = 2pi/1236

T = 5 ms

Charge on the Capacitor Q = Qo e^-*RT/2L) * cos W't + phi)

Energy across Capacitor and Inductor is

U = Q^2/2C = Qo e^-RT/L/2C = Uo e^-RT/L

in one period, as it is redcued by 6.7%

(1-0.067) Uo = Uo * e^(R*T/L)

RT/L = ln(1/0.933) = 2pi R * sqrt(C/L)

ln(0.933) = 2pi * R* sqrt(7.7*10^-6/(0.085)

R = 1.16 ohms

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Answer 2

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