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April 24, 2014

April 24, 2014

Posted by **Help** on Monday, February 27, 2012 at 10:08pm.

(a) Find the energy stored in the inductor when the current reaches its maximum value.

(b) Find the energy stored in the inductor one time constant after the switch is closed.

- Physics!!! -
**Damon**, Monday, February 27, 2012 at 10:37pmV = iR + L di/dt

i = a(1-e^-kt)

for large t

i =24/5.6 = a

so

a = 4.29

i = 4.29(1-e^-kt)

di/dt = 4.29 k e^-kt

24 = 24-24e^-kt + 2(4.29)k e^-kt

24 = 2(4.29) k

k = 24/(2*4.29) = R/L

so

i = 4.29(1-e^-(Rt/L))

current is max at great t

i max = 4.29 - 0

energy = (1/2) L i^2 =(1/2)(2)4.29^2

= 18.4 Joules

one time constant T =L/R and e^-(Rt/L) = 1/e = .368

i = 4.29 (1-.368) = 4.29*.632 = 2.71 amps

energy = (1/2)(2)2.71^2 = 7.35 Joules

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