Capacitors Physics - Capacitors

Find the equivalent capacitance of the syatem shown in figure between the points a and b.

A 100pF capacitor is charged to a potential difference of 24V. It is connected to an uncharged capacitor of capacitance 20pF. What will be the new potential difference across the 100pF capacitor?

Two conducting spheres of radii R₁ and R₂ are kept widely separated from each other. What are their individual capacitances? If the spheres are connected by a metal wire, what will be the capacitance of the combination? Think in terms of series-parallel connections.

A cylindrical capacitor is constructed using two coaxial cylinders of the same length 10cm and of radii 2mm and 4mm:

1. Calculate the capacitance.
2. Another capacitor of the same length is constructed with cylinders of radii 4mm and 8mm. Calculate the capacitance.

A point charge Q is placed at the origin. Find the electrostatic energy stored outside the sphere of radius R centred at the origin.

Suppose, one wishes to construct a 1.0 farad capacitor using circular discs. If the separation between the discs be kept at 1.0mm, what would be the radius of the discs?

A metal sphere of radius R is charged to a potential V:

1. Find the electrostatic energy stored in the electric field within a concentric sphere of radius 2R.
2. Show that the electrostatic field energy stored outside the sphere of radius 2R equals that stored within it.

When 1.0 × 10¹² electrons are transferred from one conductor to another, a potential difference of 10V appears between the conductors. Calculate the capacitance of the two-conductor system.

A capacitor with stored energy 4.0J is connected with an identical capacitor with no electric field in between. Find the total energy stored in the two capacitors.

The dielectric constant decreases if the temperature is increased. Explain this in terms of polarization of the material.

The plates of a parallel-plate capacitor are given equal positive charges. What will be the potential difference between the plates? What will be the charges on the facing surfaces and on the outer surfaces?

When a dielectric slab is gradually inserted between the plates of an isolated parallel-plate capacitor, the energy of the system decreases. What can you conclude about the force on the slab exerted by the electric field?

A parallel-plate capacitor has plates of unequal area. The larger plate is connected to the positive terminal of the battery and the smaller plate to its negative terminal. Let Q₊ and Q_- be the charges appearing on the positive and negative plates respectively:

1. Q₊ > Q_-
2. Q₊ = Q_-
3. Q₊ < Q_-
4. The information is not sufficient to decide the relation between Q₊ and Q_-.

Figure shows two capacitors connected in series and joined to a battery. The graph shows the variation in potential as one moves from left to right on the branch containing the capacitors:

1. C₁ > C₂
2. C₁ = C₂
3. C₁ < C₂
4. The information is not sufficient to decide the relation between C₁ and C₂.

A dielectric slab is inserted between the plates of an isolated charged capacitor. Which of the following quantities will remain the same?

1. The electric field in the capacitor.
2. The charge on the capacitor.
3. The potential difference between the plates.
4. The stored energy in the capacitor.

Convince yourself that parts (a), (b) and (c) of figure are identical. Find the capacitance between the points A and B of the assembly.

If the above capacitor is connected across a 6.0V battery, find:

1. The charge supplied by the battery.
2. The induced charge on the dielectric.
3. The net charge appearing on one of the coated surfaces.