Question

A parallel plate capacitor is constructed from two plates of different areas. If this capacitor is initially uncharged and then connected to a battery, how will the amount of charge on the big plate compare to the amount of charge on the small plate?

Short answer

Answer: The charges on the big and small plates of a parallel plate capacitor will be equal and opposite, irrespective of the sizes of the plates, because of the homogenous electric field between them and charge conservation in a closed circuit.

Step-by-step solution

Understanding the Capacitor

A parallel plate capacitor consists of two conducting plates separated by a distance. When connected to a battery, one plate gains positive charge, and the other plate gains an equal amount of negative charge. The charges on both plates will be equal and opposite.

Charging Process

When the parallel plate capacitor is connected to a battery, the battery provides positive charges to one plate and takes away an equal amount of charges from the other plate, making it negatively charged. This process continues until the potential difference across the plates becomes equal to the battery's EMF.

Amount of Charge on Plates

In the given exercise, the capacitor has two plates with different areas. However, charges will still distribute uniformly on both plates as the electric field between them is homogenous. Therefore, the charges on both plates will be equal and opposite, keeping in mind that the total charges on the connected components in a closed circuit remain conserved.

Conclusion

The charges on the big and small plates of a parallel plate capacitor will be equal and opposite, irrespective of the sizes of the plates, because of the homogenous electric field between them and charge conservation in a closed circuit.