How Should a Capacitor Be Filled Horizontally to Match Its Vertical Capacitance?

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SUMMARY

A vertical parallel-plate capacitor filled halfway with a dielectric of 1.97 must be filled to 50% horizontally to achieve equal capacitance when positioned horizontally. The dielectric constant directly influences the capacitance, and the geometry of the capacitor plays a crucial role in determining the required fill percentage. The analysis confirms that maintaining the same dielectric material and adjusting the fill level ensures equivalent capacitance in both orientations.

PREREQUISITES
  • Understanding of capacitor fundamentals
  • Knowledge of dielectric materials and their constants
  • Familiarity with parallel-plate capacitor equations
  • Basic principles of capacitance in different orientations
NEXT STEPS
  • Study the effects of dielectric constants on capacitance calculations
  • Learn about the geometry of capacitors and their impact on performance
  • Explore the relationship between fill percentage and capacitance in various configurations
  • Investigate practical applications of capacitors in electronic circuits
USEFUL FOR

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

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1. A vertical parallel-plate capacitor is half filled with a dielectric for which the dielectric constant is 1.97 (Fig. P26.70a). When this capacitor is positioned horizontally, what percentage of it should be filled with the same dielectric (Fig. P26.70b) so that the two capacitors have equal capacitance?

| | _______________
| |
|-+-| --------------------
|++| ++++++++++++ one is filled standing | | while one is
|++| -------------------- perpendicular to that

Homework Equations



I don't even know were to start...

The Attempt at a Solution



yup. Thanks for anything :)
 
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