Finding energy stored in capacitors without solving for current

[zorro]

Homework Statement

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?

 

[Antiphon]

Yes. At T=inf the current through the capacitors is zero.

 

[SammyS]

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 R_{2[/SUB, but the voltage drop across R3 is zero since there is no current through it.}

 

[zorro]

So you mean voltage drop across any capacitor is V ?

 

[SammyS]

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?

 

[zorro]

Its V/3
Thank you!

 

[SammyS]

Its V/3
Thank you!

Correct !