Parallel plate capacitors and dielectrics

A material used between the plates of a capacitor has a dielectric constant of 7.0

State what is meant by a dielectric constant of 7.0

Figure 3 shows a circuit that is used to charge and discharge a capacitor.

The battery has negligible internal resistance.

The two resistors in the circuit are identical.

The capacitor is fully charged and the switch is then moved from position A to position B at time t = 0

Figure 4 shows the variation of the microammeter reading with t until t = 120 s.

The time constant of the discharging circuit is T.

Determine T using Figure 4.

Electronic engineers consider a capacitor to be fully discharged when t = 5 T.

The capacitor is fully discharged and then the switch is moved from position B to position A as shown in Figure 3.

Draw, on Figure 5, the variation of the microammeter reading with time after the switch is moved to position A. In Figure 5, the time is 0 at the instant when the switch is moved to position A.

A parallel-plate capacitor X with the plates separated by air has a capacitance of 100 μF.

Another parallel-plate capacitor Y has plates that are double the height of the plates of X.

The plates of Y have the same separation and the same width as the plates of X. The space between the plates of Y is filled with a material of dielectric constant 3.0

What is the capacitance of Y ?

An air-filled parallel-plate capacitor and a resistor are connected in series across the terminals of a battery. The plates of the capacitor are then moved further apart.

This change results in

A polar molecule is in an external electric field.

Which diagram shows the orientation of the polar molecule?

Capacitor X of capacitance C has square plates of side length l and separation d and is

Capacitor Y has square plates of side length 3l and separation and is made with a

What is the capacitance of Y ?

A parallel plate capacitor is connected across a battery and the energy stored in the capacitor is E. Without disconnecting the battery, the separation of the plates is halved.

What is the energy now stored in the capacitor?

A capacitor of capacitance 63 pF is made from two parallel metal plates separated by an air gap. The capacitor is charged so that it stores a charge of 7.6 × 10⁻¹⁰ C; it is then isolated.

A sheet of mica of dielectric constant 6.0 is inserted between the plates so that it completely fills the space between them. The mica does not discharge the capacitor and does not change the separation of the plates.

Explain what is meant by a dielectric constant of 6.0

Mica is made up of polar molecules. As the mica is inserted, the capacitance of the capacitor changes.

Explain how the polar molecules cause this change in capacitance.

Calculate the difference between the initial energy stored by the capacitor and the energy stored when the mica has been fully inserted.

Figure 1 shows the structure of a variable capacitor used for measuring angular movement. The capacitor consists of two semicircular metal plates. These plates are parallel and are separated by an air gap.

To vary the capacitance, one of the plates is rotated through an angle θ using the spindle. The other plate remains fixed.

Sketch a graph on Figure 2 to show how the capacitance C varies with θ as the spindle is turned through 360°. When θ is 0°, the plates completely overlap.

In one situation, the variable capacitor is too large for the available space.

The same maximum capacitance is required using plates that have half the diameter of the original capacitor.

Explain, with numerical detail, two ways in which this can be achieved.

When a parallel-plate capacitor is connected across a battery, the energy stored in the capacitor is W.

The battery remains connected as the distance between the capacitor plates is halved.

What is the energy now stored in the capacitor?

A parallel-plate capacitor is made using a sheet of dielectric material between, and in contact with, two plates. The properties of four sheets of dielectric material are shown.

Which sheet will produce the maximum capacitance?

A parallel-plate capacitor is made by inserting a sheet of dielectric material between two plates. Both plates are in contact with the sheet.

Which relative permittivity and sheet thickness give the greatest capacitance?

An air-filled parallel-plate capacitor is charged from a source of emf. The electric field has a strength E between the plates. The capacitor is disconnected from the source of emf and the separation between the isolated plates is doubled.

What is the final electric field between the plates?

A parallel-plate capacitor has square plates of length l separated by distance d and is filled with a dielectric.

A second capacitor has square plates of length 2 l separated by distance 2 d and has air as its dielectric.

Both capacitors have the same capacitance.

What is the relative permittivity of the dielectric in the first capacitor?

Which row correctly identifies the charge on the plates and the electric field strength between the plates?

What is the capacitance of a capacitor with square plates of side 2l separated by a