Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Leakage in a dielectric. Two parallel plates of a capacitor have equal and opposite charges $Q .$ The dielectric has a dielectric constant $K$ and a resistivity $\rho .$ Show that the "leakage" current $I$ carried by the dielectric is given by $I=Q / K \epsilon_{0} \rho .$ (Note: See Section 18.8 for a review of capacitors with dielectrics.)

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$=\frac{Q}{\varepsilon_{0} K \rho}$

Physics 102 Electricity and Magnetism

Chapter 19

Current, Resistance, and Direct-Current Circuit

Electric Charge and Electric Field

Gauss's Law

Electric Potential

Capacitance and Dielectrics

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Electromagnetic Induction

Cornell University

University of Washington

McMaster University

Lectures

10:31

A capacitor is a passive two-terminal electrical component that stores electrical energy in an electric field. The effect of a capacitor is known as capacitance. The electrical charge stored in a capacitor is proportional to the potential difference between its terminals. A capacitor is defined as an electrical component that can store an electric charge. The effect of a capacitor is known as capacitance. The charge on a capacitor is directly proportional to the potential difference across its terminals. The unit of capacitance in the International System of Units (SI) is the farad (F), defined as one coulomb per volt. In electrical engineering, a common symbol for capacitance is the lowercase Greek letter "rho" (?). The capacitance of a capacitor is also expressed in farads.

18:38

In physics, electric flux is a measure of the quantity of electric charge passing through a surface. It is used in the study of electromagnetic radiation. The SI unit of electric flux is the weber (symbol: Wb). The electric flux through a surface is calculated by dividing the electric charge passing through the surface by the area of the surface, and multiplying by the permittivity of free space (the permittivity of vacuum is used in the case of a vacuum). The electric flux through a closed surface is zero, by Gauss's law.

01:27

Leakage in a Dielectric. T…

01:51

A parallel plate capacitor…

00:44

The dielectric material be…

04:22

02:36

(II) A parallel-plate capa…

07:22

05:14

A capacitor has two parall…

02:13

A parallel-plate capacitor…

03:58

An air-filled parallel-pla…

So we have ah capacitor with the destruction of the plates D on the area, off the plates. Hey, now, let's start with capacitance. You know that accident is area by distance. I'm scared, it'll or not. And you know that Resistance Israel held by a So which is, in this case, road D by a as you can see the length Yes, d in this case. So now that you know our assistance, we know the leakage current current is simply ward age by residents. And that is we buy art which is ruled by a so that we may buy now, as you can see, I'm sorry this is D l used in this case. As you can see, there is a body in these two expressions so we can replace everybody using this expression. If you leave a radio on silence and everything to the others other, we get ideas he called to see like a solano. So this is we've I wrote times everybody. Hence that is we buy the times. They can replace a body with this. See if I care not no. We know that voltage times capacitance is charged. That is how capacitance is in fact, different. If Aston's is charged by weight, which means one times capacitance What All these times capacitance is charge. So this gives us current is equal to charge Times s alone, not row. Okay, no, the question ends here, but it's interesting to think about first thing. We can obviously decrease leakage current by maximizing this quantity, that is, we wantto make video where they resisted the product of a study on developed constant is very large. And the second thing is, as you can see is current is the cue by DT. In fact, current is minus dick. You reality is equal to Hugh Bison Constant. Let's go. If you remember how these equations call this, he gets exponentially. If you find it out. You can see that queue often. Is Cunard Times minus Steve, I tell. Hence any real capacitor with really leakage current, it loses its charge on Hence, the world. Did it hold exponentially? Even if the circuit is open, even if you just leave it off, give us our league night. It'll slowly decay

View More Answers From This Book

Find Another Textbook

Numerade Educator

09:24

write the main procedures involved in the dry preservation of cockroach.

02:52

c) An iron boat floating in sea rusts more compared to a boat submerged (sin…

01:43

A pendulum makes 50 complete swings in 2 min and 40 sec how much it take…

03:30

A CaCO3 solution shows the transmittance of 25% when taken in a cell of 1.5 …

01:34

What is relative permittivity? equal to the absolute permittivity Oratio of …