Question

4. + -12 points SerCP11 20.7.P.051.MI. A 24-V battery is connected in series with a resistor and an inductor, with R = 5.0 N and L = 2.4 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. Need Help? Read It

Answer 1

Solution) V = 24 v

R = 5 ohm

L = 2.4 H

(a) Energy stored in inductor when current reaches maximum value , U = ?

U = (1/2)(L)(i^2)

i = V/R

i = (24)/(5)

i = 4.8 A

U = (1/2)(2.4)(4.8^2)

U = 27.6 J

(b) Energy stored after one time constant , U' = ?

i' = i( 1 - e^(-t/T))

Here t = T

i' = i(1 - e^(-T/T))

i' = i(1 - e^(-1))

i' = 4.8( 1 - e^(-1))

i' = 3.03 A

U' = (1/2)(L)(i'^2)

U' = (1/2)(2.4)(3.03^2)

U' = 11 J