Inclined parallel plate capacitor

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SUMMARY

The discussion centers on the behavior and formulas related to inclined parallel plate capacitors, specifically addressing the capacitance of a rectangular capacitor compared to a parallelogram-shaped capacitor. Participants confirm that as the plate separation approaches zero, the capacitance values of both configurations converge. Key approximations used in the derivation include ##\text{tan}\alpha\approx\alpha## and ##z_{1}\approx z_{0}+x_{1}## for small angles. The importance of plate separation and height in determining capacitance is also emphasized.

PREREQUISITES
  • Understanding of capacitor fundamentals, including capacitance and plate separation.
  • Familiarity with geometric configurations of capacitors, specifically rectangular and parallelogram shapes.
  • Basic knowledge of calculus and approximations in physics, particularly small angle approximations.
  • Experience with electrical engineering concepts related to parallel plate capacitors.
NEXT STEPS
  • Research the derivation of the capacitance formula for inclined parallel plate capacitors.
  • Explore the impact of plate separation on capacitance in various capacitor configurations.
  • Study small angle approximations and their applications in electrical engineering.
  • Investigate the differences in capacitance between various geometric shapes of capacitors.
USEFUL FOR

Electrical engineers, physics students, and anyone interested in advanced capacitor design and analysis will benefit from this discussion.

mertcan
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hi, I wonder that inclined plate capacitor formula is the formula in last picture I shared? I am not sure because there are not enough examples about that ?
 
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Is there a derivation before this? It would help since I'm not completely sure what assumptions the authors are making.
 
NFuller said:
Is there a derivation before this? It would help since I'm not completely sure what assumptions the authors are making.
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Here is the total work here.
ALSO I have ANOTHER question : initially we are used to see parallel capacitor of which plates are perpendicular to horizontal plane ( A CAPACITOR LIKE RECTANGULAR ), but let's think a parallel capacitor of which plates make an SAME angle with horizontal plane ( A CAPACITOR LIKE PARALLELOGRAM ).
My question is : A CAPACITOR LIKE RECTANGULAR of which height is same with A CAPACITOR LIKE PARALLELOGRAM has same capacitance with CAPACITOR LIKE PARALLELOGRAM??
 
Last edited:
mertcan said:
My question is : A CAPACITOR LIKE RECTANGULAR of which height is same with A CAPACITOR LIKE PARALLELOGRAM has same capacitance with CAPACITOR LIKE PARALLELOGRAM??
Are you asking at what plate separation the capacitance of a normal parallel plate capacitor equals that of a capacitor with both plates at some common angle?

If so, then the two capacitors will approach the same value as the plate separation approaches zero.
mertcan said:
hi, I wonder that inclined plate capacitor formula is the formula in last picture I shared? I am not sure because there are not enough examples about that ?
They appear to be using two approximations here ##\text{tan}\alpha\approx\alpha## and ##z_{1}\approx z_{0}+x_{1}## for small ##\alpha##.
 
NFuller said:
Are you asking at what plate separation the capacitance of a normal parallel plate capacitor equals that of a capacitor with both plates at some common angle?

If so, then the two capacitors will approach the same value as the plate separation approaches zero.
Yes you are so close to my question but only the plate separation angle is important ? Are not the distance between plates and height of plates (or capacitor) important ? Should they are same also?
 
@NFuller could you have a look at my last question for your last reply?
 
mertcan said:
Are not the distance between plates and height of plates (or capacitor) important ? Should they are same also?
Yes, as the plate separation increases, the capacitors will decrease their capacitance.
 

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