What is the Equivalent Capacitance in This Circuit?

In summary, the problem asks to find the equivalent capacitance for the given circuit. Using the formula for series and parallel capacitors, the solution is found to be 4C/3. However, a mistake was made in the calculation, resulting in only half of the correct answer being obtained. The error was corrected, resulting in the final answer of 4C/3.
  • #1
Acuben
64
0

Homework Statement



http://yfrog.com/mrcapdg

http://img819.imageshack.us/img819/1172/capd.th.gif

Find equivalent capacitance
answer is 4C/3

Homework Equations


whatever is in parenthesis is subscript
formula1: series: 1/C(eq)= 1/C(1) + 1/C(2) + 1/C(3) + ...
formula2: parallel: C(eq)=C(1)+C(2)+...

formula3: V=Q/C

The Attempt at a Solution



because of symmetry I decided that 3C has 0 charge (0q) and that top part has same voltage as the bottom part

charge split top and bottom equally

so I solved the problem "as if" 3C doesn't exist
so on the top series I get C/3 (using formula 1) and C/3 for bottom as well since it's in symmetry
and top and bottom form parallel so I get
2C/3 using formula 2

which is only half the answer

><
 
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  • #2
For top branch 1/Ceff = 1/C + 1/2C = ?
 
  • #3
o thanks for pointing that out, I made simple algebra mistake ^^
 

FAQ: What is the Equivalent Capacitance in This Circuit?

What is equivalent capacitance?

Equivalent capacitance refers to the total capacitance of a circuit or system of capacitors that can be replaced by a single capacitor, with the same effect on the circuit as the original set of capacitors.

How do you calculate equivalent capacitance?

To calculate equivalent capacitance, you can use the formula Ceq = C1 + C2 + C3 + ..., where Ceq is the equivalent capacitance and C1, C2, C3, etc. are the individual capacitances of the capacitors in the circuit. Alternatively, you can use the parallel and series combination formulas for capacitors depending on the circuit configuration.

What is the difference between series and parallel capacitors?

Series capacitors are connected end-to-end and have the same voltage across them, while parallel capacitors are connected side-by-side and have the same charge on them. In a series circuit, the equivalent capacitance is less than the smallest individual capacitor, while in a parallel circuit, the equivalent capacitance is greater than the largest individual capacitor.

Why is finding equivalent capacitance important?

Finding equivalent capacitance is important because it allows us to simplify complex circuits into a single equivalent capacitor, making it easier to analyze the behavior of the circuit. Additionally, it can help us determine the energy stored in the circuit and the voltage and current across each capacitor.

Can capacitors in a circuit have different capacitance values?

Yes, capacitors in a circuit can have different capacitance values. In fact, most circuits are made up of capacitors with different capacitance values. This is because different capacitors can be used for different purposes, such as filtering, timing, and energy storage.

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