A 24.0-V battery is connected in series with a resistor and an inductor, with R

Question

A 24.0-V battery is connected in series with a resistor and an inductor, with R = 2.00 ? and L = 7.00 H, respectively.

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

(b) Find the energy stored in the inductor at an instant that is a time interval of one time constant after the switch is closed.
  
You appear to have confused the factor that relates the current after one time constant of closing the switch with the factor by which it would decay in one time constant if the source of emf were suddenly bypassed. J

Explanation / Answer

a)

maximum current = V/ R

I = 24 / 2

I = 12 amp

then by using the formula

U = 0.5 * L * I^2

U = 0.5* 7 * 12^2

U = 504 J

the energy stored in the inductor when current is maximum is 504 J

b)

at t = time constant

I = Imax ( 1 - e^-1)

I = 12 ( 1 - 0.368)

I = 7.6 amp

and then by using the formula

U = 0.5 * L * I^2

U = 0.5 * 7 * 7.6^2

U = 202.16 J

so the energy stored in the inductor at time interval of one time constant is 202.16J

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