Do two capacitors of different plate areas gain the same or different amounts of charge when connected to the same battery?

When two capacitors with different plate areas are connected to the same battery, they will gain different amounts of charge. The reason lies in the relationship between the capacitance of a capacitor, the charge it stores, and the voltage applied to it.

The capacitance of a parallel plate capacitor is given by the formula:

C=ε0A/d

Where:

  • ε0\varepsilon_0 is the permittivity of free space,
  • A is the area of one of the plates,
  • is the separation between the plates.

When connected to a battery, the voltage V across each capacitor is the same, and the charge stored on a capacitor is related to its capacitance by:

Q=C⋅V

Since the two capacitors have different areas (and thus different capacitances), the capacitor with the larger plate area will have a higher capacitance and will store more charge, while the one with the smaller area will store less charge. Therefore, the two capacitors will gain different amounts of charge, with the one having the larger plate area storing more charge.

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