Capacitance

Question 1

What happens to the current as a capacitor is charged? What does a graph of charging current versus time as a capacitor is charged look like?

Answer 1

1) It decreases, approaching zero when the capacitor is fully charged
2) It is an exponential decay curve (graph has a ‘constant ratio property’, it reduces by the same factor in equal time intervals). The gradient of the curve at any point is the rate of change of current at that moment in time, which decreases as time passes

Question 2

What happens when a dielectric material is used in the gap between two metal plates of a capacitor? Why does this increase the capacitance of the capacitor?

Answer 2

1) The materials used as dielectrics contain polar molecules. Before the capacitor is charged the polar molecules have random orientations, but on experiencing the electric field of a charged capacitor, they rotate and align themselves with the field.
2) This polarisation creates an internal electric field that partially cancels the electric field created by the charge on the plates, which reduces the potential difference across the capacitor. To return the pd to its original value, more charge must be added onto the plates. This creates a greater potential difference hence increasing capacitance.

Question 3

What is a dielectric?

Answer 3

A layer of electrical insulator that separates two metal plates

Question 4

What happens if the pd applied across the plates of a capacitor is too large?

Answer 4

The insulating material of the dielectric will break down electrically and conduction will occur across the gap

Question 5

What are two useful facts about the time constant?

Answer 5

• 1/e of the original current value is approximately 37% of Ιο (max current)
• A reasonable estimate for the time for a capacitor to fully charge is 5 time constants = 5RC

Question 6

When does a capacitor stop charging?

Answer 6

When the potential difference between the plates is equal to the emf of the cell

Question 7

In a capacitor discharge circuit, the pd and the charge Q on the capacitor all decrease exponentially with time with the same time constant RC. How can this be summarised?

Answer 7

The gradients of the ln Q versus time graph and the ln V versus time graph for capacitor discharge are all equal: gradient = - 1/time constant

Question 8

Experiments show that the capacitance C of a parallel-plate capacitor Is directly proportional to… and inversely proportional to…

Answer 8

1) … the area A of the overlap of the plates

2) … the plate separation d

Question 9

What is an electrolytic capacitor and how does it work?

Answer 9

They consist of two aluminium plates separated by a thin sheet of paper soaked in aluminium borate. When the capacitor is charged up, a chemical reaction occurs which deposits a layer of aluminium oxide on the positive plate. This thin oxide layer acts as the dielectric.

Question 10

What does the gradient of the tangent at a point on a Q-t graph for a capacitor discharging equal?

Answer 10

The current at that point in time

Question 11

Why do lightning strikes occur?

Answer 11

When a thunder cloud forms, positive ions collect at the top of the cloud and elections collect near the bottom. The electrons at the bottom of the cloud exert a repulsive force on the free electrons in the surface of the earth and push them deeper into the ground, leaving a net positive charge on the surface of the earth in the area below the cloud. The negative lower section of the cloud and the surface of the earth effectively becomes a charged capacitor. Air is an insulator and in dry conditions requires an electric field of 3000 kVm^-1. However in the damp conditions where thunder clouds are formed, an electric field of 300 kVm^-1 will make the air conduct, this leads to a lightning strike.

Question 12

Capacitance can be measured using…

Answer 12

… a capacitance meter

Question 13

What is relative permittivity known as?

Answer 13

The dielectric constant. It is a number with no units and varies with different materials

Question 14

What is a variable air capacitor? Give an example of where they are used

Answer 14

1) A capacitor made up of interleaved parallel metal plates. The amount of plate surface that overlaps and the plate separation can be changed by rotating the rotor into the stator
2) In a radio tuner

Question 15

A capacitor with a large capacitance can store…

A capacitor with a small capacitance…

Answer 15

1) … a large amount of charge with a relatively low pd across its plates
2) … would not store as much charge even with a large pd across its plates

Question 16

What is the time constant? What is it useful for?

Answer 16

1) The time for the charging current to fall to 1/e of its original value
2) Calculating time delays required in electronic circuits

Question 17

What does the area between the curve and the time axis of an I-t graph equal?

Answer 17

The charge that has flowed off the capacitor

Question 18

On a graph of charge stored on a capacitor versus the protein applied across its plates, what is the gradient of the graph equal to? What does the nature of line plotted demonstrate?

Answer 18

1) The capacitance of the capacitor because Q = CV

2) The capacitance of a particular capacitor is constant

Question 19

What is the benefit of electrolytic capacitors over parallel-plate capacitors?

Answer 19

Parallel-plate capacitors usually have capacitances less that 100μF, electrolytic capacitors are capable of storing much more charge and can have capacitances up to 0.1F

Question 20

How can capacitors of different capacitance be produced?

Answer 20

By changing the overlap of the plates and the plate separation

Question 21

Capacitors can be particularly useful when a high power output is required for a short time interval. How does the capacitor in a flash camera work?

Answer 21

The capacitor is charged to its full pd by a battery. The capacitor then discharges through a xenon flash tube in a very short period of time, converting the electrical energy stored in the capacitor to light energy emitted from the flash tube. The power output is high but lasts less than a millisecond.

Question 22

What does the capacitance of a parallel-plate capacitor depend on?

Answer 22

The area of overlap of the plates, the separation of the plates, as well as the dielectric between the plates

Question 23

What property must a material used as a dielectric have? Give some examples of suitable materials

Answer 23

1) It must be a good electrical insulator to prevent the flow of electrons
2) Polyester, polycarbonate, mica and polyethene

Question 24

What is the capacitance of a capacitor defined as?

Answer 24

The charge stored per unit potential difference across the plates

Question 25

How can you store more charge on a capacitor?

Answer 25

By increasing the potential difference across the capacitor. This can be done by connecting two cells in series to its terminals rather than one.

Question 26

What is the fundamental function of a capacitor?

Answer 26

To store electric charge

Question 27

For many capacitor applications the rate that the capacitor becomes charged and subsequently discharged needs to be carefully controlled, how can this be achieved? When would this be needed?

Answer 27

1) By connecting a resistor in series with the capacitor. The greater the resistance of the resistor, the more slowly the charging or discharging takes place
2) When a time delay is required

Question 28

What is the relative permittivity of a dielectric? In the case of a capacitor, the relative permittivity is…

Answer 28

1) A factor by which the electric field between two charges is decreased by the presence of the dielectric, relative to a vacuum.
2) … equal to the factor by which the capacitance is increased when using that material as a dielectric compared with a similar capacitor with a vacuum between its plates

Question 29

What are the units of capacitance?

Answer 29

• The farad (F), 1F is equal to 1CV^-1
• The farad is a large unit, most capacitors have small capacitance values so prefixes such as μ, n and p are usually required