[2 days left] What’s wrong with your cloud strategy? Learn why multicloud solutions matter with Nimble Storage.Register Now

x
Solved

# Capacitor, with half a dielectric

Posted on 2007-12-03
Medium Priority
1,496 Views
A parallel plate capacitor has a capacitance C when there is vacuum between the plates. How does
this change if the gap between the plates is half filled with a dielectric with dielectric constant eps_r?

(The given diagram looks almost as good as this ;)

|
-----------------------------------------------------------------------
+--------------------------------+
|             Dielectric              |
+--------------------------------+
-----------------------------------------------------------------------
|

Here's my idea:

Treat the capacitor as two seperate capacitors, in parallel, like so:

|
+-----------+----------+
|                              |
---------------------      -------------------
Dielectric
---------------------      -------------------
|                             |
+-----------+----------+
|

Then through a bit of math, this gets me to:

C = C0*(1+eps_r)/2

I notice that the (1+eps_r)/2 term is the average eps_r value (as eps_r=1 in vacuum); so it would make sense.

However, [as my last question proved], it's better safe than sorry...
So is this the correct method?

(I have a quick follow up question after this)

Thanks
0
Question by:InteractiveMind
[X]
###### Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

• Help others & share knowledge
• Earn cash & points
• 3
• 2

LVL 27

Accepted Solution

d-glitch earned 2000 total points
ID: 20398269
That is correct.
The conducting plates are equipotential surfaces, so you can break them up that way.
0

LVL 27

Expert Comment

ID: 20398597
C_left  +  C_right  =  eps_0 *( A/2)/d  +  eps_r * (A/2)/d  =  (eps_0 + eps_r)*(A/2)/d
0

LVL 25

Author Comment

ID: 20398706
Oh, I thought it was:

C_left  +  C_right  =  eps_0 *( A/2)/d  +  eps_r * eps_0 * (A/2)/d  =  eps_0*(1 + eps_r)*(A/2)/d

?
0

LVL 27

Expert Comment

ID: 20398822
You arecorrect if you are dealing with relative permitivities.
0

LVL 25

Author Comment

ID: 20398852
Okay, cool.

Thank you, d-glitch.
0

## Featured Post

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Have you ever thought of installing a power system that generates solar electricity to power your house? Some may say yes, while others may tell me no. But have you noticed that people around you are now considering installing such systems in their …
This article provides a brief introduction to tissue engineering, the process by which organs can be grown artificially. It covers the problems with organ transplants, the tissue engineering process, and the current successes and problems of the tec…
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…
I've attached the XLSM Excel spreadsheet I used in the video and also text files containing the macros used below. https://filedb.experts-exchange.com/incoming/2017/03_w12/1151775/Permutations.txt https://filedb.experts-exchange.com/incoming/201…
###### Suggested Courses
Course of the Month13 days, 17 hours left to enroll