What is the initial charge of a discharging capacitor with given values?

[eurekameh]

The capacitor C = 3.00 microF at t = 0 has a stored energy U0 = 1.67 x 10^-7 J. At t = 0
the switch S is closed and the capacitor discharges through resistor R = 8700 Ohms. What's the initial charge of the capacitor?

I'm doing q0 = iRC. I'm stuck on finding what the current through the circuit is.

 

[VladiMonev]

I=Cdu/dt. You have to find the voltage on the capacitor.Since the energy before and after the commutation is equal W(0-)=W(0+). You have a relation about energy W=C*U^2/2. You find the intial value for voltage.The final value of the capacitor`s voltage is zero,because it has been discharged.So u(t)=U(0+)*e^-t/T. T=R*C-time constant for discharging the capacitor. and Qo=C*U(0-). Think that is enough

 

[eurekameh]

What do the symbols 0- and 0+ mean?

 

[VladiMonev]

0- means before the commutation and 0+ after commutation. In capacitor the voltage before and after are equal U(0-)=U(0+).Or there would be a infinite change in voltage du/dt.

 

[technician]

There are 3 versions of the equation for the energy stored on a charged capacitor :
0.5 x Q x V; 0.5 x C x V^2 ; 0.5 Q^2 /C
You could use the third one directly to find the charge, Q, on the capacitor.
You can now also calculate the voltage across the capacitor, this is the voltage at t = 0.
When S is closed the voltage is connected across the 8700Ω resistor so you should be able to calculate the initial current.
The current (and voltage) decrease exponentially ( I x e^-t/T ; and V x e^-t/T )
T is the time constant of the C R combination

 

[eurekameh]

K, thanks for the equations. I was trying to relate the voltage and the potential energy somehow, and I thought maybe U = qV. But that's only for particles, right?

 

[technician]

U = qV is certainly the way to calculate the energy of particles with charge 'q' moving through a potential difference (voltage) of V.
You have probably met eV (electron volt) as a unit of energy when the charge is that of an electron (e = 1.6 x 10^-19 C)
A really useful thing to know is that Voltage means Joule per Coulomb.
1 Volt means 1 Joule of energy given to 1Coulomb of charge when it passes through 1Volt
It will help you in lots of electricity problems if you translate 'Volt' to be 'Joule per coulomb'

 

[eurekameh]

Thanks. Units do indeed go a long way.