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Chapter 24: Problem 23

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

Expert verified
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

01

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.
02

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.
03

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.
04

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.

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Most popular questions from this chapter

Fifty parallel plate capacitors are connected in series. The distance between the plates is \(d\) for the first capacitor, \(2 d\) for the second capacitor, \(3 d\) for the third capacitor, and so on. The area of the plates is the same for all the capacitors. Express the equivalent capacitance of the whole set in terms of \(C_{1}\) (the capacitance of the first capacitor).

A parallel plate capacitor consists of square plates of edge length \(2.00 \mathrm{~cm}\) separated by a distance of \(1.00 \mathrm{~mm}\). The capacitor is charged with a \(15.0-\mathrm{V}\) battery, and the battery is then removed. A \(1.00-\mathrm{mm}\) -thick sheet of nylon (dielectric constant \(=3.0\) ) is slid between the plates. What is the average force (magnitude and direction) on the nylon sheet as it is inserted into the capacitor?

A dielectric slab with thickness \(d\) and dielectric constant \(\kappa=2.31\) is inserted in a parallel place capacitor that has been charged by a \(110 .-\mathrm{V}\) battery and having area \(A=\) \(100, \mathrm{~cm}^{2},\) and separation distance \(d=2.50 \mathrm{~cm}\). a) Find the capacitance, \(C,\) the potential difference, \(V,\) the electric field, \(E,\) the total charge stored on the capacitor \(Q\), and electric potential energy stored in the capacitor, \(U\), before the dielectric material is inserted. b) Find \(C, V, E, Q,\) and \(U\) when the dielectric slab has been inserted and the battery is still connected. c) Find \(C, V, E, Q\) and \(U\) when the dielectric slab is in place and the battery is disconnected.

A \(4.00 \cdot 10^{3}-n F\) parallel plate capacitor is connected to a \(12.0-\mathrm{V}\) battery and charged. a) What is the charge \(Q\) on the positive plate of the capacitor? b) What is the electric potential energy stored in the capacitor? The \(4.00 \cdot 10^{3}-\mathrm{nF}\) capacitor is then disconnected from the \(12.0-\mathrm{V}\) battery and used to charge three uncharged capacitors, a \(100 .-n F\) capacitor, a \(200 .-\mathrm{nF}\) capacitor, and a \(300 .-\mathrm{nF}\) capacitor, connected in series. c) After charging, what is the potential difference across each of the four capacitors? d) How much of the electrical energy stored in the \(4.00 \cdot 10^{3}-\mathrm{nF}\) capacitor was transferred to the other three capacitors?

Which of the following capacitors has the largest charge? a) a parallel plate capacitor with an area of \(10 \mathrm{~cm}^{2}\) and a plate separation of \(2 \mathrm{~mm}\) connected to a \(10-\mathrm{V}\) battery b) a parallel plate capacitor with an area of \(5 \mathrm{~cm}^{2}\) and a plate separation of \(1 \mathrm{~mm}\) connected to a \(10-\mathrm{V}\) battery c) a parallel plate capacitor with an area of \(10 \mathrm{~cm}^{2}\) and a plate separation of \(4 \mathrm{~mm}\) connected to a \(5-\mathrm{V}\) battery d) a parallel plate capacitor with an area of \(20 \mathrm{~cm}^{2}\) and a plate separation of \(2 \mathrm{~mm}\) connected to a \(20-\mathrm{V}\) battery e) All of the capacitors have the same charge.
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