Realistic Capacitor with leaking dielectric

In summary, a good capacitor has a small leakage current due to the conductive properties of the dielectric inside. To find the conductivity of the dielectric, we can set up the problem as if a resistor was connected in parallel to the capacitor and use the equations ##C=\kappa C_{0}##, ##\sigma=\frac{1}{\rho }##, and ##R=\frac{V}{I}## to solve for the conductivity.
  • #1
yango_17
60
1

Homework Statement


A realistic capacitor is almost always filled with dielectric, but invariably this dielectric will conduct just a little, and the charge stored on the capacitor's plates will "leak." Over time, quite a bit of current can leak away. A good capacitor has a small leakage current.
Consider a parallel-plate capacitor with the plates of area A and distance between them d, filled with a dielectric with the dielectric constant κ. At t=0, some charge is put on the capacitor so that it's voltage is ##V_{0}##. At some later time ##\tau =t##, the voltage on the capacitor is ##V(\tau )=\frac{V_{0}}{e}## (where e is Euler's constant). What is the conductivity σ of the dielectric?

Homework Equations


##C=\kappa C_{0}##
##\sigma=\frac{1}{\rho }##
##R=\frac{V}{I}##

The Attempt at a Solution


I would like to know how to begin to set up the problem. I'm not sure how to go about finding a relation between the voltage of the capacitor and the conductivity of the dielectric, especially when one has to take into account the "leaking" of the dielectric. Any help getting started on this problem would be appreciated. Thanks!
 
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  • #2
You can handle the leakage as if a resistor was connected parallel to the capacitor.
 
  • #3
Ah, that's a great hint. Alright, I'll see how far I can take it from here
 

1. What causes a capacitor's dielectric to leak?

The most common cause of a capacitor's dielectric leaking is aging or damage to the dielectric material. Over time, the dielectric can degrade due to environmental factors such as temperature and humidity, or from electrical stress. Damage to the dielectric can also occur during manufacturing or installation processes.

2. How does a leaking dielectric affect a capacitor's performance?

A leaking dielectric can significantly impact a capacitor's performance. It can cause a decrease in capacitance, an increase in dissipation factor, and a shift in the capacitor's electrical characteristics. This can ultimately lead to the capacitor failing to meet its intended specifications and potentially causing malfunctions in electronic circuits.

3. Can a capacitor with a leaking dielectric be repaired?

In most cases, a capacitor with a leaking dielectric cannot be repaired. Once the dielectric is damaged or degraded, it cannot be restored to its original state. Attempting to repair a leaking capacitor could also pose safety hazards and should not be done by someone without proper training and equipment.

4. How can a capacitor with a leaking dielectric be identified?

A capacitor with a leaking dielectric can be identified by conducting various tests, such as a capacitance test or a dissipation factor test. Physical signs such as bulging or discoloration of the capacitor can also indicate a leaking dielectric. It is important to regularly test and inspect capacitors to identify any potential issues.

5. How can a capacitor with a leaking dielectric be prevented?

To prevent a capacitor's dielectric from leaking, it is essential to use high-quality capacitors and follow recommended operating conditions. Avoid exposing capacitors to extreme temperatures, high humidity, or excessive electrical stress. Regular maintenance and testing can also help identify any potential issues before they become significant problems.

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