Energy Dissipation in an RC Circuit: Finding the Total Thermal Energy

[electrohau5]

Homework Statement

A capacitor C=8.00*10^-8F which has an initial charge q=1.4*10^-6C starts to discharge through a resistor R=3.00*10^6Ω at time t=0. Determine the total energy W dissipated as thermal energy in the resistor. Hint: use energy conservation.

The Attempt at a Solution

I already found U(0)=1.225e-5J (energy stored in capacitor at t=0), but how do I use energy conservation to find W?

 

[technician]

When the capacitor is completely discharged, where has the stored energy gone?

 

[electrohau5]

When the capacitor is completely discharged, where has the stored energy gone?

are you saying all the energy goes to heat so U=W?

 

[technician]

Yes! ...are you certain this was the whole question? The value of the resistance does not affect the energy transfer...do you know what it will affect?

 

[electrohau5]

Yes! ...are you certain this was the whole question? The value of the resistance does not affect the energy transfer...do you know what it will affect?

yes, thank you, it was the whole question, but there were parts before it.
This was part e I believe.

I was a little skeptical about U=W because this part is worth 7 points, which makes U=W seem too simple.

 

[technician]

What was the whole question?

 

[electrohau5]

(it was actually part d. my bad!)

A capacitor C=8.00*10^-8F which has an initial charge q=1.4*10^-6C starts to discharge through a resistor R=3.00*10^6Ω at time t=0. Determine the following:

a. (3points) the time constant (tau) of the circuit.
b. (5points) the current i at t=(tau)
c. (4points) the energy U(0) at t=0
d. (7points) the total energy W dissipated as thermal energy in the resistor
e. (6points) the time which the energy U is equal to 25% of U(0)

I figured out the other parts, but d looked suspicious since it is worth more than all other questions but apparently has the same answer as c.

 

[electrohau5]

Yes! ...are you certain this was the whole question? The value of the resistance does not affect the energy transfer...do you know what it will affect?

oh, and for your question there, I believe resistance affects the time constant RC which affects the rate of the capacitor's discharging.