Equivalent Capacitors and their charges:

In summary, the problem involves finding the value of C in a circuit where the total equivalent capacitance (C-eq) is known to be 9.22 microfarads. After attempting different approaches, it is determined that the combination of 12μF and 8.35μF capacitors are in series and their equivalent is in parallel with 4.5 μF. This combination is then in series with C, and the entire combination is in parallel with 7.22 μF. By setting up and solving the correct equations, the value of C can be found.
  • #1
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Homework Statement


Hi, I'm trying to solve this problem on MasteringPhysics:

This circuit is given, and it says C-eq for the circuit is 9.22 microfarads:

http://img143.imageshack.us/img143/3475/walker4ech21pr118.jpg

The question is to find C in the figure knowing C-eq is 9.22 microfarads.

Homework Equations


C-eq series = 1/C-eq = 1/C1 + 1/C2 + ...
C-eq parallel = C1 + C2 + C3 ...

The Attempt at a Solution



At first I tried to take the three center capacitors to be parallel (The 7.22, 4.25, and 8.35) and find the Ceq of them and then take the other two to be in a series with this C-eq. But when I do that, I get a negative value for C.

Then I tried to take the C, 12.0 uF, and 8.35 uF to be in a series, combine them and then have that C-eq be parallel to the other two, but that also gives me a negative value.


Thank you.
 
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  • #2
In the circuit diagram no three capacitors are either series or parallel.
Here 12μF and 8.35μF are in series. Equivalent of these capacitors is in parallel with 4.5 μF.
Combination of these capacitors is in series with C. Finally all the above is in parallel with 7.22 μF. The whole combination is equal to 9.22 μF. Write down the correct equations and solve for C.
 
  • #3


It seems like you are on the right track with your attempts to solve this problem. However, it is important to remember that capacitors in series do not add up the same way as resistors in series. In fact, the formula for equivalent capacitance in series is: 1/C-eq = 1/C1 + 1/C2 + ... (without the negative sign).

Therefore, to find the equivalent capacitance of the three center capacitors (7.22, 4.25, and 8.35), you would need to use this formula and then add it in parallel to the remaining two capacitors (12.0 and 8.35 uF). This should give you a positive value for C.

Additionally, it is important to note that the negative value you obtained in your attempts may be due to a calculation error. Make sure to double check your calculations and units to ensure accuracy. Good luck!
 

1. How do you calculate the equivalent capacitance of capacitors in series?

To calculate the equivalent capacitance of capacitors in series, you can use the formula 1/Ceq = 1/C1 + 1/C2 + 1/C3 + ... + 1/Cn, where C1, C2, C3, etc. are the individual capacitances of the capacitors. This formula is based on the fact that the charge on each capacitor in a series circuit is the same, and the total voltage is divided among the capacitors.

2. What is the rule for calculating the equivalent capacitance of capacitors in parallel?

The rule for calculating the equivalent capacitance of capacitors in parallel is to simply add all the individual capacitances together, resulting in Ceq = C1 + C2 + C3 + ... + Cn. This is because in a parallel circuit, the voltage across each capacitor is the same, and the total charge is divided among the capacitors.

3. How does the charge on each capacitor change when they are connected in series?

When capacitors are connected in series, the charge on each capacitor will be the same. This is because they are connected in a single pathway, and therefore, the same amount of charge flows through each capacitor. The individual capacitances will determine how much charge each capacitor can hold.

4. What happens to the charge on each capacitor when they are connected in parallel?

When capacitors are connected in parallel, the total charge on each capacitor will be different. This is because they are connected in separate pathways, and the charge is divided among the capacitors based on their individual capacitances. The voltage across each capacitor will remain the same.

5. Can you have an equivalent capacitance that is larger than any of the individual capacitances?

Yes, it is possible to have an equivalent capacitance that is larger than any of the individual capacitances. This can happen when capacitors are connected in parallel, as the equivalent capacitance is calculated by adding all the individual capacitances together. In this case, the combined capacitance will be larger than any of the individual capacitances.

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