Calculating Energy Stored in a Capacitor: Is There a Shortcut Method?

In summary, the conversation discusses finding the energy stored in each capacitor after closing K1, K2, and K3. One method involves finding the current and using I = CdV/dt, but it is lengthy. Another method involves recognizing that at t = infinity, the current through the capacitors is zero. This leads to a simpler circuit and the voltage drop across R3 is zero. The conversation concludes with the correct answer being V/3.
  • #1
zorro
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Homework Statement



attachment.php?attachmentid=32853&stc=1&d=1299454780.jpg


Long time after closing K1,k2 and k3 the energy stored in each capacitor is?


The Attempt at a Solution



My method is to find out an expression for the current through the capacitor (of net capacitance 2C) at any time t and use I = CdV/dt to find out V across it at t=inf.

However this method appears to be very long. Is there any shortcut?
 

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  • #2
Yes. At T=inf the current through the capacitors is zero.
 
  • #3
Antiphon said:
Yes. At T=inf the current through the capacitors is zero.
Also notice: that will leave you with a fairly simple circuit. The capacitors in combination with R3 are in parallel with R2[/SUB, but the voltage drop across R3 is zero since there is no current through it.
 
  • #4
So you mean voltage drop across any capacitor is V ?
 
  • #5
Abdul Quadeer said:
So you mean voltage drop across any capacitor is V ?
No.

As t → ∞ :

The only current flowing is through R1 and R2.

What is the voltage drop across R2?
 
  • #6
Its V/3
Thank you!
 
  • #7
Abdul Quadeer said:
Its V/3
Thank you!
Correct !
 

What is a capacitor?

A capacitor is an electronic component that stores electrical energy in the form of an electric field. It consists of two conductive plates separated by a dielectric material.

How does a capacitor store energy?

When a capacitor is connected to a power source, such as a battery, one plate becomes positively charged and the other becomes negatively charged. This creates an electric field between the plates, storing energy in the form of separated charges.

What is the unit of measurement for energy stored in a capacitor?

The unit of measurement for energy stored in a capacitor is joules (J), which is the same unit used to measure energy in other forms, such as mechanical or thermal energy.

How does the capacitance affect the amount of energy stored in a capacitor?

The capacitance of a capacitor, which is determined by its physical characteristics, directly affects the amount of energy it can store. A higher capacitance means the capacitor can store more energy, while a lower capacitance means it can store less energy.

Can a capacitor store an unlimited amount of energy?

No, a capacitor has a limit to the amount of energy it can store. Once it reaches its maximum capacity, it cannot store any more energy and may even become damaged. It is important to select a capacitor with the appropriate capacitance for the desired energy storage needs.

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