Solving for Equal Capacitors in Parallel: Potential of Each

In summary, when two capacitors of equal capacitance, with one charged to potential V and the other completely discharged, are connected in parallel, the potential of each capacitor will be V/sqrt(2). This can be determined by finding the charge on the charged capacitor (Q), the total charge on the two capacitors when connected (Q'), the capacitance of the two capacitors when connected (C'), and the potential of the connected capacitors (V'). This can all be expressed in terms of C and V and then simplified to V/sqrt(2).
  • #1
vipulsilwal
26
0

Homework Statement


2 capacitors of equal capacitance one charged to potential V, and other completely discharged. when the are connected in parallel what would be the potential of each one of them.

Homework Equations



E=1/2 (C.V^2)

The Attempt at a Solution


as they are connected in parallel potential of each wud be same... now by conservation of energy i got answer V/sqrt(2)
am i right??
 
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  • #2
vipulsilwal said:

Homework Statement


2 capacitors of equal capacitance one charged to potential V, and other completely discharged. when the are connected in parallel what would be the potential of each one of them.

Homework Equations



E=1/2 (C.V^2)

The Attempt at a Solution


as they are connected in parallel potential of each wud be same... now by conservation of energy i got answer V/sqrt(2)
am i right??
What is the charge, Q, on the charged capacitor (in terms of C and V)?
What is the total charge, Q', on the two capacitors when they are connected together?
What is the capacitance, C', of the two capacitors when connected together (in terms of C)?
What is the potential V' (in terms of Q' and C')?
Now express the answer in terms of C and V.

AM
 
  • #3
When you connect the two capacitors in parallel, energy will be lost due to the charges moving through the resistive wires. So conservation of energy doesn't apply in this case. But the total number of charges is conserved. So follow Andrew Mason's steps and you will get the right answer.
 

1. How do I solve for the potential of each capacitor in parallel?

To solve for the potential of each capacitor in parallel, you need to first determine the total capacitance of the circuit. This can be done by adding the individual capacitances of the capacitors. Then, use Ohm's Law (V=IR) to calculate the total current flowing through the circuit. Finally, use the equation V=Q/C to calculate the potential of each capacitor, where Q is the charge on each capacitor and C is the individual capacitance.

2. Can I use Kirchhoff's Laws to solve for equal capacitors in parallel?

Yes, you can use Kirchhoff's Laws to solve for equal capacitors in parallel. Kirchhoff's Laws state that the sum of all currents entering a node is equal to the sum of all currents leaving the node. This can be applied to parallel circuits by considering the total current flowing into the node and the individual currents flowing through each capacitor.

3. Do I need to know the individual capacitance values to solve for equal capacitors in parallel?

Yes, you need to know the individual capacitance values to solve for equal capacitors in parallel. The total capacitance of the circuit is dependent on the individual capacitance values, and without this information, you cannot accurately calculate the potential of each capacitor.

4. What happens to the potential of each capacitor when equal capacitors are connected in parallel?

When equal capacitors are connected in parallel, the potential of each capacitor will be the same. This is because parallel capacitors have the same voltage across them, and according to Kirchhoff's Laws, the potential difference across each capacitor in a parallel circuit is equal to the total potential difference of the circuit.

5. Can I use the same method to solve for unequal capacitors in parallel?

No, the method for solving for equal capacitors in parallel is not suitable for solving for unequal capacitors in parallel. This is because the total capacitance and total current in the circuit will be different for unequal capacitors, and the potential of each capacitor will not be the same. In this case, a more complex calculation involving the individual capacitance values and the voltage divider rule must be used.

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