Exercise
https://texercises.raemilab.ch/exercise/simple-double-capacitor/
Question
Solution
Short
Video
\(\LaTeX\)
No explanation / solution video to this exercise has yet been created.

Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
A double capacitor consists of two fixed outer plates and two connected inner plates. The inner plates can be moved from left to right see figure which causes a change to the distances a and b between the two parallel plate capacitors C_ and C_. Show that the capacitance of the two capacitors in series does not dep on the position of the inner plates. center includegraphicswidth.textwidth#image_path:basic-doublcapacitor# center

Solution:
The two capacitors are C_ varepsilon_ fracAa C_ varepsilon_ fracAb The da+b of the two distances is constant. We can therefore write a x d b -x d with xin. The series capacitance is given by sscCs leftfracC_+fracC_right^- leftfracx dvarepsilon_ A+frac-x dvarepsilon_ Aright^- varepsilon_fracAdleftx+-xright^- varepsilon_fracAd It turns out that the capacitance is indepent of the position of the inner plates and corresponds to a parallel plate capacitor with the same plate area and a distance equal to the of the two distances a and b.
Report An Error
You are on texercises.raemilab.ch.
reCaptcha will only work on our main-domain \(\TeX\)ercises.com!
Meta Information
\(\LaTeX\)-Code
Exercise:
A double capacitor consists of two fixed outer plates and two connected inner plates. The inner plates can be moved from left to right see figure which causes a change to the distances a and b between the two parallel plate capacitors C_ and C_. Show that the capacitance of the two capacitors in series does not dep on the position of the inner plates. center includegraphicswidth.textwidth#image_path:basic-doublcapacitor# center

Solution:
The two capacitors are C_ varepsilon_ fracAa C_ varepsilon_ fracAb The da+b of the two distances is constant. We can therefore write a x d b -x d with xin. The series capacitance is given by sscCs leftfracC_+fracC_right^- leftfracx dvarepsilon_ A+frac-x dvarepsilon_ Aright^- varepsilon_fracAdleftx+-xright^- varepsilon_fracAd It turns out that the capacitance is indepent of the position of the inner plates and corresponds to a parallel plate capacitor with the same plate area and a distance equal to the of the two distances a and b.
Contained in these collections:

Attributes & Decorations
Branches
Electrostatics
Tags
capacitance, capacitor, electrostatic, parallel plate capacitor, series circuit
Content image
Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Proof
Creator by
Decoration