What is the Equivalent Capacitance of a Single Capacitor Setup?

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SUMMARY

The equivalent capacitance of a single capacitor setup, specifically when considering capacitors C1 and C2, is determined to be C1. In this arrangement, C2 does not contribute to the overall capacitance due to the symmetry of the circuit, resulting in zero voltage across C2. Therefore, the effective capacitance remains unchanged from the configuration without C2, confirming that the answer is C1.

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  • Understanding of capacitor configurations, specifically series and parallel arrangements.
  • Familiarity with the equations for calculating equivalent capacitance: Cparallel and Cseries.
  • Basic knowledge of circuit symmetry and its effects on voltage distribution.
  • Ability to interpret circuit diagrams and analyze capacitor behavior within them.
NEXT STEPS
  • Study the principles of capacitor behavior in series and parallel configurations.
  • Learn about circuit symmetry and its implications on voltage and charge distribution.
  • Explore advanced capacitor configurations and their equivalent capacitance calculations.
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Sami Lakka
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Homework Statement


What is the equivalent capacitance of the arrangement shown in figure. (Answer is C1)


Homework Equations


Cparallel = C1+C2+...Cn
Cseries = 1/(1/C1+1/C2+...+1/Cn)


The Attempt at a Solution

 

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Sami Lakka said:

Homework Statement


What is the equivalent capacitance of the arrangement shown in figure. (Answer is C1)


Homework Equations


Cparallel = C1+C2+...Cn
Cseries = 1/(1/C1+1/C2+...+1/Cn)


The Attempt at a Solution

It is easier to see what is happening if you change the drawing to a square with 2 C1s on each side in series and a C2 attached across the middle (from points between the C1s).

By the symmetry of the circuit, you can see that there is 0 voltage across the C2 capacitor. So the C2 really does nothing to change the capacitance of the circuit - ie. it never stores charge. So the capacitance is the same as the circuit without C2.

AM
 

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