Equivalent Capacitance in a circuit

In summary, the equivalent capacitance of the four capacitors in the given circuit is approximately 3.11 mF. The correct equation for finding equivalent capacitance in a parallel circuit is Ceq=(C1+C2+C3...), not (C1+C3)(C2+C4)/(C1+C2+C3+C4).
  • #1
carpelumen
10
0

Homework Statement


In the circuit shown in the figure the voltage of the battery is 15.0 V, and the capacitors have the following capacitances: C1 = 2.32 mF, C2 = 2.25 mF, C3 = 4.85 mF, C4 = 4.89 mF
What is the equivalent capacitance of the four capacitors?

http://tinypic.com/r/24dn5oi/8
Two sets of series capacitors that are parallel to each other

Homework Equations


Ceq=(1/C1+1/C2+1/C3...)^-1 ---- series
Ceq=(C1+C2+C3...) --- parallel

The Attempt at a Solution


Ceq=(C1+C3)(C2+C4)/(C1+C2+C3+C4)
=(7.17)(7.14) / 14.31
= 3.58 mF

According to online homework system, it's wrong. Is my equation incorrect?
 
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  • #2
I think you've got the series/parallel actions backwards. Do capacitors add directly when in series or when in parallel?
 
  • #3
Perhaps show us how you got...

Ceq=(C1+C3)(C2+C4)/(C1+C2+C3+C4)
 
  • #4
I think you've got the series/parallel actions backwards. Do capacitors add directly when in series or when in parallel?

I don't think that's his problem because his relevant equations..

Ceq=(1/C1+1/C2+1/C3...)^-1 ---- series
Ceq=(C1+C2+C3...) --- parallel

... are correct. Capacitors add in parallel.
 
  • #5
CWatters said:
... are correct. Capacitors add in parallel.

Right, which is what led me to wonder how he got a term (c1+c3)
 
  • #6
Is the answer near 3.13 mF
 
  • #7
harley davidson said:
Is the answer near 3.13 mF
Very close to that, yes.
 
  • #8
Even closer to 3.11 :)
 

What is equivalent capacitance in a circuit?

Equivalent capacitance in a circuit is the combined capacitance of multiple capacitors connected in a circuit. It represents the total amount of charge a circuit can store.

How is equivalent capacitance calculated?

The equivalent capacitance of capacitors connected in series can be calculated by adding the reciprocals of individual capacitances and taking the reciprocal of the sum. For capacitors connected in parallel, the equivalent capacitance is the sum of individual capacitances.

What is the significance of equivalent capacitance in a circuit?

Equivalent capacitance is important in determining how a circuit will behave. It affects the time constant and charging/discharging of the circuit, as well as the energy stored in the circuit.

Can equivalent capacitance be negative?

No, equivalent capacitance cannot be negative as it represents the total capacitance of the circuit which is always a positive value. However, it can be zero if all the capacitors in the circuit are disconnected.

How does the arrangement of capacitors affect the equivalent capacitance?

The arrangement of capacitors in a circuit can significantly affect the equivalent capacitance. When capacitors are connected in parallel, the equivalent capacitance increases, while in series, it decreases. Therefore, the arrangement should be considered when calculating the equivalent capacitance.

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