Physics!!!
posted by Help on .
A 24V battery is connected in series with a resistor and an inductor, with R = 5.6 Ω and L = 2.0 H, respectively.
(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.

V = iR + L di/dt
i = a(1e^kt)
for large t
i =24/5.6 = a
so
a = 4.29
i = 4.29(1e^kt)
di/dt = 4.29 k e^kt
24 = 2424e^kt + 2(4.29)k e^kt
24 = 2(4.29) k
k = 24/(2*4.29) = R/L
so
i = 4.29(1e^(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