Question

A damper LC circuit loses 7.7% of it's electromagnetic energy per cycle to thermal energy.
If L= 85 mH and C= 8.10 micro Farad. What is the value if R .

anyone up .Tired of your solution just need correct answer .get few time left .thanks

Answer 1

inductance, L=85 mH

capacitance, C=8.1 uF

let,

initially energy stored is Uo

and

per one cycle,

energy reduced, U=Uo-7.7% of Uo

U=Uo-(7.7/100)*(Uo)

U=Uo*(0.923) ----(1)

==>

here,

Uo=qo^2/2C and U=q^2/2C

and q=qo*e^(-(R/2L)T) --(2)

==>

from (1) and (2)

U=Uo*(0.923)

q^2/2C=(qo^2/2C)*(0.923)

qo^2*e^(-R*T/L)/2C=(qo^2/2C)*(0.923)

e^(-R*T/L)=(0.923)

RT/L=ln(1/0.923) --(3)

here,

T=2pi/W

T=2pi/(1/sqrt(LC))

T=2pi*sqrt(LC) --(4)

from (3) and (4)

R*2pi*sqrt(LC)/L = ln(1/0.923)

R*2pi*sqrt(C/L) = ln(1/0.923)

R*2pi*sqrt((8.1*10^-6)/(85*10^-3))=ln(1/0.923)

===> R=1.306 ohms

resistance, R=1.306 ohms