What Is the Energy Stored in the Circuit at Steady State?

[ACE_99]

Homework Statement

We are given: R₁= 1$$\Omega$$
R₂= 2$$\Omega$$
L = 3 mH
C = 500 $$\mu$$F

If the voltage is kept at 4V what is the energy stored in the circuit after it has reached a steady state. There is a link posted to the circuit provided below.

Homework Equations

energy stored in capacitor = 1/2Cv²
energy stored in inductor = 1/2Li²

The Attempt at a Solution

Since you are given all the values you can just plug into the formula to find the energy stored in the capacitor. I got 0.004J. For the inductor I determined the current that flows through it which is 4V / 2$$\Omega$$ = 2A. I then used this value to compute the energy stored in the inductor, for that I got 0.006J. The total energy would be the sum of the two.

This seems to be a simple problem but I'm just wondering if its a trick question since they want to know what the energy stored is after a long period of time.

 

[Phrak]

The energies (1/2)Li^2 and (1/2)Cv^2 are the steady state values for stored energy. You're result looks correct to me.

 

[ACE_99]

Great thanks.

 

[CEL]

Steady state means after an infinite time. Generally we consider that after 5 time constants the circuit reaches steady state. That is the meaning of a long period of time