Charging two capacitors then putting them in parallel

In summary, two capacitors, C_1 = 13 uF and C_2 = 26 uF, are initially charged to 20 V each and then connected in parallel, with the positive plate of C_1 connected to the negative plate of C_2 and vice versa. The equivalent capacitance is 39 uF and the charges on each capacitor, Q1 and Q2, are 87 and 170 uC, respectively. The potential difference across each capacitor is not specified.
  • #1
Linus Pauling
190
0
1. Capacitors C_1 = 13 uF and C_2 = 26 uF are each charged to 20 V, then disconnected from the battery without changing the charge on the capacitor plates. The two capacitors are then connected in parallel, with the positive plate of C_1 connected to the negative plate of C_2 and vice versa.

Afterward, what is the charge on each capacitor?



2. Q = VC, equivalent C for parallel capacitors add linearly



3. I know Q1 and Q2 are 87 and 170 uC, respectively. I know that the equivalent capacitance is simple 39 uF. But I still don't see how these charges were obtained.
 
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  • #2
Linus Pauling said:
The two capacitors are then connected in parallel, with the positive plate of C_1 connected to the negative plate of C_2 and vice versa.

If they are connected in parallel, what is the potential difference across each capacitor?
 

1. How does charging two capacitors and putting them in parallel affect the overall capacitance?

When two capacitors are charged and then placed in parallel, the overall capacitance increases. This is because the total charge on the parallel combination is the sum of the charges on each capacitor, and the voltage across the combination is the same as the voltage across each individual capacitor. Therefore, the capacitance of the parallel combination is equal to the sum of the individual capacitances.

2. What happens to the individual charges and voltages of the capacitors when they are placed in parallel?

When capacitors are placed in parallel, the individual charges on each capacitor remain the same, while the voltage across each capacitor becomes equal. This is because capacitors in parallel have the same potential difference, and the total charge on the parallel combination is the sum of the charges on each individual capacitor.

3. Can two capacitors with different capacitances be placed in parallel?

Yes, capacitors with different capacitances can be placed in parallel. The overall capacitance of the parallel combination will be equal to the sum of the individual capacitances. However, the voltage across each capacitor will be different, with the capacitor with the smaller capacitance having a higher voltage.

4. How does the energy stored in the capacitors change when they are placed in parallel?

When capacitors are placed in parallel, the total energy stored in the combination increases. This is because the energy stored in a capacitor is directly proportional to its capacitance, and the parallel combination has a larger capacitance than each individual capacitor. Therefore, the parallel combination can store more energy than each individual capacitor.

5. What is the potential difference across the parallel combination of two capacitors?

The potential difference across the parallel combination of two capacitors is equal to the potential difference across each individual capacitor. This is because the voltage across capacitors in parallel is the same, and the total voltage of the parallel combination is equal to the voltage of each individual capacitor.

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