In a purely inductive AC circuit as shown in the figure, ? V max = 100 V. (a) Th

Question

In a purely inductive AC circuit as shown in the figure, ?Vmax = 100 V.

(a) The maximum current is 8.00 A at 70.0 Hz. Calculate the inductance L.
_________________H

(b) At what angular frequency ? is the maximum current 3.50 A?
__________________rad/s

A 24.0-V battery is connected in series with a resistor and an inductor, with R = 4.00 ? and L = 6.20 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.
__________________J

In a purely inductive AC circuit as shown in the figure, ?Vmax = 100 V. In a purely inductive AC circuit as shown in the f (a) The maximum current is 8.00 A at 70.0 Hz. Calculate the inductance L. _________________H (b) At what angular frequency ? is the maximum current 3.50 A? __________________rad/s A 24.0-V battery is connected in series with a resistor and an inductor, with R = 4.00 ? and L = 6.20 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. __________________J

Explanation / Answer

1.

a)

Inductive reactance

XL=V/I =100/8 =12.5 ohms

Since

XL=2pi*f*L

12.5=2pi*70*L

L=0.0284 H

b)

XL=100/3.5 =28.57 ohms

since XL=WL

=>28.57=W*0.0284

W=1005.33 rad/s

2.

a)

Io=E/R =24/4 =6 A

Eo=(1/2)*L*Io2=(1/2)*6.2*62=111.6 J

b)

I=Io[1-e-t/T]

Given t=T

I=6[1-e-1] =3.79 A

E=(1/2)*6.2*3.792=44.6 J

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