Capacitors and capacitance

A capacitor is initially uncharged and is then charged using a constant current. This is achieved by reducing the resistance of a variable resistor R as the charge on the capacitor increases.

The capacitor has a capacitance of 300 mF and is fully charged in a time t = 100 s. The cell has an emf of 2.0 V and negligible internal resistance. The charging current is 6.0 mA.

What is the resistance of R at t = 30 s ?

Figure 8 shows a circuit used to investigate the charge and discharge of a capacitor of capacitance C using resistors of resistances R₁ and R₂.

The battery has an emf of 6.0 V and negligible internal resistance.

Show that the time taken for the capacitor to charge from 2.0 V to 4.0 V is

The capacitor is fully discharged. The capacitor is then charged until the potential difference (pd) across it is 4.0 V. Figure 9 shows the variation with time of the ammeter reading as the capacitor is charged.

Show that the capacitance of the capacitor is about 1 × 10⁻⁴ F.

When the pd reaches 4.0 V the switch is immediately set to discharge the capacitor. When the pd reaches 2.0 V the switch is immediately set to charge the capacitor.

Figure 10 shows how the pd across the capacitor varies with time.

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 switch S allows capacitor C to be completely charged by a cell and then completely discharged through an ammeter. The emf of the cell is 4.0 V and it has negligible internal resistance. The capacitance of C is 0.40 F and there are 8000 charge−discharge cycles every

What are the magnitude and direction of the average conventional current in the ammeter?

An uncharged capacitor is connected to a power supply which supplies a constant current of 10 μA.

After 100 ms, the potential difference across the capacitor is 5.0 kV.

What is the capacitance of the capacitor?

Figure 3 shows an arrangement used to investigate the repulsive forces between two identical charged conducting spheres. The spheres are suspended by non-conducting thread.

Each sphere has a mass of 3.2 × 10⁻³ kg and a radius of 20 mm. The distance d is 40 mm.

The capacitance of a sphere of radius r is 4πε₀r.

Each sphere is charged by connecting it briefly to the positive terminal of a high-voltage supply, the other terminal of which is at 0 V. After this has been done the charge on each sphere is 52 nC.

Calculate the potential of one of the spheres.

The charged spheres in Figure 3 are at equilibrium.

Draw labelled arrows on Figure 3 to show the forces on sphere B.

Suggest a solution to one problem involved in the measurement of d in Figure 3.

Show that the magnitude of the electrostatic force on each sphere is about 4 × 10⁻³ N

A student measures the angle θ when the apparatus in Figure 3 is at equilibrium. The student records θ as 7°.

Discuss whether this measurement is consistent with the other data in this investigation.

The student says that the gravitational force between the two spheres has no significant effect on the angle at which the spheres are in equilibrium.

Deduce with a calculation whether this statement is valid.

A 1.0 µF capacitor initially stores 15 µC of charge. It then discharges through a 25 Ω resistor.

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

State what is meant by a capacitance of 370 F

The charging of a 370 F capacitor is investigated using the circuit shown in Figure 4 Both meters in the circuit are ideal.

The power supply of emf 9.8 V has a negligible internal resistance. The capacitor is initially uncharged. When the switch is closed at time t = 0 charge begins to flow through resistor R. The time constant of the charging circuit is 1.0 s

Calculate the resistance of R.

Identify, with the symbol X on Figure 5, the potential difference (pd) across the capacitor when the switch has been closed for 2.0 s Sketch the graph that shows how the pd varies from t = 0 to t = 2.0 s

Calculate the time taken for the charging current to fall to half its initial value.

Calculate the time taken for the charge on the capacitor to reach 3.0 mC

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?

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?

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