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

In summary, the question asks to determine the total energy W dissipated as thermal energy in a resistor with a capacitor starting at a certain charge and discharging through the resistor. The value of the resistance does not affect the energy transfer, but it does affect the time constant of the circuit. The energy U at t=0 is equal to 25% of U(0) at a certain time.
  • #1
electrohau5
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0

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?
 
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  • #2
When the capacitor is completely discharged, where has the stored energy gone?
 
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  • #3
technician said:
When the capacitor is completely discharged, where has the stored energy gone?

are you saying all the energy goes to heat so U=W?
 
  • #4
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?
 
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  • #5
technician said:
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.
 
  • #6
What was the whole question?
 
  • #7
(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.
 
  • #8
technician said:
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.
 

What is an RC circuit?

An RC circuit is a circuit that contains a resistor (R) and a capacitor (C) connected in series. It is used to control the flow of electric current and store electrical energy.

How does energy dissipation occur in an RC circuit?

Energy dissipation in an RC circuit occurs due to the conversion of electrical energy into heat energy. As the capacitor charges and discharges, heat is generated in the resistor due to the flow of electric current.

What factors affect the rate of energy dissipation in an RC circuit?

The rate of energy dissipation in an RC circuit is affected by the resistance of the resistor, the capacitance of the capacitor, and the voltage applied to the circuit. A higher resistance, capacitance, or voltage will result in a higher rate of energy dissipation.

How can energy dissipation be minimized in an RC circuit?

Energy dissipation in an RC circuit can be minimized by using a resistor with a lower resistance value, a capacitor with a lower capacitance value, or a lower voltage. Additionally, using a higher quality resistor or capacitor can also help reduce energy dissipation.

What are some practical applications of RC circuits and energy dissipation?

RC circuits and energy dissipation are commonly used in electronic devices such as radios, amplifiers, and filters. They are also used in power supplies to regulate voltage and prevent damage from power surges. In addition, energy dissipation in RC circuits is an important concept in the study of electrical engineering and circuit analysis.

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