Energy stored by a capacitor

An isolated solid conducting sphere is initially uncharged. Electrons are then transferred to the sphere.

State and explain the location of the excess electrons.

Figure 3 shows how the electric potential V varies with distance r from the centre of the sphere. The radius of the sphere is 0.10 m.

The magnitude of the electric field strength E is related to V by E =.

Determine, using this relationship, the magnitude of the electric field strength at a distance 0.30 m from the centre of the sphere.

State an appropriate SI unit for your answer.

The sphere acts as a capacitor because it stores charge at an electric potential.

Show that the capacitance of the sphere is approximately 1 × 10⁻¹¹ F.

Electrons leak away from the sphere with time and the amount of energy stored by the sphere decreases. At one instant, the magnitude of the electric potential of the sphere has fallen to 1.0 × 10⁶ V.

Calculate, for this instant, the change in the energy stored by the sphere.

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 fully charged capacitor of capacitance 2.0 mF discharges through a 15 kΩ resistor.

What fraction of the stored energy remains after 1.0 minute?

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 10 μF capacitor stores 4.5 mJ of energy. It then discharges through a 25 Ω resistor.

What is the maximum current during the discharge of the capacitor?

A 1.0 µF capacitor is charged for 20 s using a constant current of 10 µA.

What is the energy transferred to the capacitor?

The graph shows the variation of potential difference (pd) with charge for a capacitor while it is charging.

Which statement can be deduced from the graph?

What is the change in the energy stored by the capacitor?