Three identical capacitors are connected in parallel. If the total charge stored in the system is Q, what is the charge on each individual capacitor?
Q/3
To solve this problem, we need to understand how capacitors behave when connected in parallel. In a parallel connection:
- The voltage across each capacitor is the same.
- The total charge stored is the sum of the charges stored in each capacitor.
If each capacitor has a capacitance of C and the voltage across them is V, then the charge Q_i on each capacitor is given by:
Q_i = C \cdot V
Since all capacitors have the same capacitance and are connected in parallel, each will store an equal amount of charge. If the total charge stored in the system is Q, and there are three capacitors, then by the symmetry of the setup, the charge on each capacitor is:
Q_i = \frac{Q}{3}
Therefore, the charge on each individual capacitor is Q/3.
The correct answer is Q/3.
Let's evaluate the given options:
- \frac{Q}{9}: Incorrect, as explained above, each capacitor will have \frac{Q}{3} charge.
- Q: Incorrect, Q is the total charge, not the charge on an individual capacitor.
- 3Q: Incorrect, this would imply the total charge is split in some non-standard way.
- \frac{Q}{3}: Correct, this is consistent with the parallel configuration.
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