6.1 Capacitors

Question 1

Define capacitor.

Answer 1

An electrical component that stores charge on two separated metallic plates. An insulator called a dielectric is placed between the plates to prevent charge from travelling across the gap.

Question 2

What is a dielectric?

Answer 2

An insulator which is placed between the plates of a capacitor to prevent charge from travelling across the gap.

Question 3

Define capacitance.

Answer 3

The charge stored (Q) per unit potential difference (V), across the two plates of a capacitor.

Question 4

A fully uncharged capacitor is connected to a DC power supply.

[1] What initially occurs?
[2] How does this initial activity affect the charge on each capacitor plate?
[3] What happens in the end?

Answer 4

There will be a brief current as the power supply draws electrons from one plate, and deposits them on the other plate.

This leaves the first plate with charge +Q and the second with charge -Q. These charges will be equal and opposite due to the conservation of charge.

Current will flow in the circuit until the potential difference between the plates is equal to that of the EMF of the power supply.

Question 5

Aside from insulation, what is the other purpose of the dielectric?

Answer 5

To increase the capacitance of the device by polarizing in the electric field, and effectively increasing the charge stored on the plates.

Question 6

State Kirchhoff’s voltage law.

Answer 6

The sum of the EMFs in any closed loop in a circuit is equal to the sum of PDs in the same loop.

V = V1 + V2 + V3 + …

Question 7

What is the formula for calculating the combined capacitance of capacitors in series?

Answer 7

(1/C) = (1/C1) + (1/C2) + (1/C3) + …

Question 8

State Kirchhoff’s current law.

Answer 8

The total current flowing into a point in a circuit must be equal to the total current flowing out of that point.

Question 9

What is the formula for calculating the combined capacitance of capacitors in parallel?

Answer 9

C = C1 + C2 + C3 + …

Question 10

Work must be done by the power supply to deposit negatively charged electrons onto the negative plate. Why is this?

Answer 10

Like charges repel (according to Coulomb’s law)

Question 11

Work is done to remove electrons from the positive plate of a capacitor. Why is this?

Answer 11

Negative charges are attracted to positive regions.

Question 12

Consider a graph with Voltage (V) against Charge Stored (Q).

What kind of graph can we expect to see?

Answer 12

A straight line graph passing through the origin.

Question 13

Consider a graph with Voltage (V) against Charge Stored (Q).

What does the area under the graph represent?

Answer 13

The area under the graph represents the work done in charging up the capacitor, and so it represents the energy stored in the capacitor.

W = 1/2 QV
W = 1/2 V^2 C
W = Q^2 / 2C

Question 14

What are capacitors used for? What in particular does this make them useful for?

Answer 14

They are used to store and discharge large quantities of energy in a short time period.
This makes them useful for short pulses of energy (eg camera flashes)

Question 15

What are two major applications of capacitors?

Answer 15

Uninterrupted power supplies (UPSs), which are used as backup power supplies when the mains electricity supply fails.

Converting AC into DC.

Question 16

How can capacitors be used in converting AC to DC?

Answer 16

A sinusoidal AC signal can be passed through a full wave rectifier to make the current flow in one direction. It can then be passed through a smoothing circuit, where a capacitor stores energy as the PD rises and discharges as it falls, which provides a more constant current. Pass the signal through another smoothing circuit and another until the voltage is effectively constnat.

Question 17

What is the formula for the time constant?

Answer 17

𝜏 = CR

Question 18

Define time constant.

Answer 18

The time taken for the voltage to discharge to 37% of its original value.

Question 19

What must be done to find the halving time?

Answer 19

Multiply the time constant by ln2

Question 20

Why is capacitance directly proportional to the area of the plates?

Answer 20

The capacitance depends on the number of electrons that can be stored on the negative plate. Greater area means a greater number of electrons can be stored.

Question 21

Why is the capacitance inversely proportional to the separation distance?

Answer 21

The attraction between charges on the negative and positive plates depends on the separation of the plates. Greater separation distance means less attraction as they are further away from each other.