Chapter 23 - Capacitors

Question 1

What is a capacitor?

What are capacitors used for?

Answer 1

A capacitor is an electric device consisting of two metal plates separated by an insulator (dielectric).
Capacitors are used to store charge/energy.

Question 2

Explain how a capacitor is charged.

Answer 2

When a capacitor is connected to a power supply, the electrons flow from the negative terminal to the positive terminal of the battery. Electrons flow from the negative terminal of the cell to the positive plate of the capacitor.

The two plates now have equal and opposite charge.

When the p.d. across the two plates is equal to the emf of the battery, the current in the circuit falls to zero. The capacitor is then fully charged.

Question 3

What is the time constant?

Answer 3

τ = RC

The time taken for the charge, pd or current to decrease to e^-1 of its initial value.

If t = RC is put into the discharging equation then,

Q = Q0e^-1
V = V0e^-1
I = I0e^-1

Question 4

How can the time constant be found from a log-linear graph?

Answer 4

Taking the natural log of both sides of the capacitor discharge equation gives the equation of a straight line.
Thus a graph of lnQ against t gives a straight line.
The time constant can be calculated from the gradient as the gradient = -1/RC.

Question 5

What is the time taken for the charge, pd or current of a discharging capacitor to become half of the value it was when it was fully charged?

Answer 5

Time to halve, T˅1/2 = 0.69RC

Question 6

Describe the action of a simple polar molecule in a dielectric in the presence of an electric field of a parallel plate capacitor.

Answer 6

If a dielectric is placed between two oppositely charged plates then any unpolarised molecules within the dielectric will become polarised by the oppositely charged plates.
The surface of the dielectric facing the positive plate therefore gains a negative charge due to the movement of electrons towards that side (vice versa).

Question 7

Inserting a dielectric increases the _____ and ________ of the capacitor.

Answer 7

Inserting a dielectric increases the charge and capacitance of the capacitor (due to the polarisation of the molecules within the dielectric)

Question 8

What is the equation for the relative permittivity of dielectric material (a.k.a. dielectric constant)

Answer 8

εr = Q/Q0
or
εr = C/C0