Parallel Capacitors: Homework Solution for 9 μF Charge

In summary, a 9 μF capacitor is fully charged to 200 V and then connected in parallel with an uncharged 3 μF capacitor. The 3 μF capacitor becomes fully charged and is then discharged. The remaining charge on the 9 μF capacitor can be calculated using the equation Q=CV. To reduce the charge on the 9 μF capacitor to below 50% of its initial charge, this process would have to be repeated multiple times. The potential difference between the plates of the 9 μF capacitor would change as the charges are redistributed during each connection and disconnection.
  • #1
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1

Homework Statement



A capacitor of capacitance 9 μF is fully charged from a 200 V dc supply. The
capacitor is now disconnected from the supply and connected in parallel with an
uncharged 3 μF capacitor. Once the 3 μF capacitor is fully charged, it is removed
and discharged. a) What charge remains on the 9 μF capacitor? b) How many
times would this process have to be repeated in order to reduce the charge on the 9
μF capacitor to below 50% of its initial charge? c) What would be the pd between
the plates of the 9 μF capacitor now be?


Homework Equations



Q=CV


The Attempt at a Solution



a) I said that the 3μF capacitor will be fully charged when the voltage across both capacitors is the same,let's say Vx.

Since energy has to be conserved then Ei=Ef therefore

C1V^2 = C1Vx^2 + C2Vx^2 <=> Q1' = 1.5588*10^-3 C . Am i doing this correct ?
 
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  • #2
Unfortunately, much as in elastic collisions of masses, connection of capacitors in parallel is not an operation that conserves energy; some energy is lost when the charges get shuffled into their new configuration.

What is conserved through the connection operation, though, is charge.
 
  • #3
Thank you very much !
 

FAQ: Parallel Capacitors: Homework Solution for 9 μF Charge

What are parallel capacitors?

Parallel capacitors are two or more capacitors connected in a circuit where each capacitor has one end connected to a common point and the other ends connected to separate points. This arrangement allows for the sharing of charge between the capacitors, resulting in a larger total capacitance.

What is the formula for calculating the equivalent capacitance of parallel capacitors?

The formula for calculating the equivalent capacitance of parallel capacitors is Ceq = C1 + C2 + C3 + ..., where Ceq is the equivalent capacitance and C1, C2, C3, etc. are the individual capacitances of each capacitor.

How do I calculate the charge stored in a parallel capacitor arrangement?

To calculate the charge stored in a parallel capacitor arrangement, you can use the formula Q = CV, where Q is the charge, C is the equivalent capacitance, and V is the voltage applied to the capacitors.

Can the charge on each capacitor in a parallel arrangement be different?

Yes, the charge on each capacitor in a parallel arrangement can be different. The amount of charge on each capacitor will depend on its individual capacitance and the voltage applied to the circuit.

How can parallel capacitors be used in practical applications?

Parallel capacitors are commonly used in electronic circuits to increase the overall capacitance and store more charge. They can also be used to filter out unwanted frequencies in a circuit and to stabilize voltage levels.

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