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

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Discussion Overview

The discussion revolves around calculating the energy stored in a circuit at steady state, given specific component values (resistors, inductor, capacitor) and a voltage. The focus is on applying relevant equations for energy storage in capacitors and inductors, and understanding the implications of steady state in this context.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant presents a problem involving a circuit with specified resistances, inductance, and capacitance, and seeks to calculate the energy stored after reaching steady state.
  • The participant uses the formulas for energy stored in a capacitor and an inductor, providing specific numerical results for each.
  • Another participant confirms the calculations as correct, indicating agreement on the approach taken.
  • A further reply clarifies that steady state implies a condition reached after an infinite time, typically approximated by five time constants in practical scenarios.

Areas of Agreement / Disagreement

There appears to be agreement on the calculations presented, but the interpretation of what constitutes steady state and the implications of time constants may not be fully resolved among all participants.

Contextual Notes

The discussion does not explicitly address potential assumptions about the circuit configuration or the definitions of steady state and time constants, which may affect the interpretation of the results.

ACE_99
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Homework Statement


We are given: R1= 1[tex]\Omega[/tex]
R2= 2[tex]\Omega[/tex]
L = 3 mH
C = 500 [tex]\mu[/tex]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[tex]\Omega[/tex] = 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.

circuit.jpg
 
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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.
 
Great thanks.
 
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
 

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