What is the Equivalent Capacitance of a Single Capacitor Setup?

AI Thread Summary
The equivalent capacitance of the given capacitor arrangement is determined to be C1. By analyzing the circuit's symmetry, it is concluded that the capacitor C2 does not affect the overall capacitance, as it experiences zero voltage and does not store charge. The relevant equations for parallel and series capacitance were noted, but the specific configuration simplifies the problem. Therefore, the final answer remains C1, as C2's presence does not alter the circuit's behavior. Understanding the impact of symmetry in capacitor arrangements is crucial for solving such problems effectively.
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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