Chapter 23 - Capacitors

Question 1

What is a capacitor?

Answer 1

Device designed to store charge

Question 2

How does a capacitor work?

Answer 2

Two parallel metal plates placed near each other and connected to a battery. Electrons move through the battery and are forced from it’s negative terminal of the battery onto one side of the plates. An equal number of electrons leave the other plate and return to the battery via its positive terminal - so each plate gains an opposite and equal charge.

Question 3

Draw the symbol for a capacitor

Answer 3

Question 4

How do you calculate the charge,Q, on a capacitor when charging

Answer 4

Q = It where t = time after switch is closed

Question 5

How can a capcitor’s pd be measured when charging?

Answer 5

By using a high resistance voltmeter in parallel with the capacitor and using the variable resistor to keep the current constant, either:

• Use a stopwatch and measure reading at measured times
• Use a data logger

Question 6

What would a graph of charge against pd graph for a capacitor look like?

Answer 6

Straight line passing through the origin

Question 7

Define capacitance and give an equation

Answer 7

The capacitance (C) of a capacitor is defined as the charge stored per unit pd

C = Q/V

unit: Farad (F)

Question 8

How is the energy stored in a capacitor obtained from a graph?

Answer 8

Charge against pd graph
Area under the graph = energy stored = 1/2QV

as energy stored is equal to the work done to force charge on to the plates

Question 9

Why does a capacitor store energy as it’s being charged?

Answer 9

Electrons are forced onto one of the plates and taken of the other. Energy stored as electric potential energy

Question 10

What is the equation for the increase in energy stored when the seperation of two parallel plates increases?

Answer 10

1/2 QE delta d

where d = seperation between the parallel plates

Question 11

Why does energy stored increase when seperation distance between the parallel plates is increased?

Answer 11

Work is done to force plates apart, overcoming the electrical attraction between the 2 plates.

Question 12

Draw the graph for a discharging curve of charge against time

Answer 12

Question 13

In what proportionality does current, charge and pd of a capacitor decrease with respect to time when discharging through a fixed resistor?

Answer 13

Exponentially

Question 14

What actually happens in a discharge circuit?

Answer 14

• as soon as switch is closed, ‘large’ current flows and p.d. across capacitor drops
• as charge flows from one plate to the other through the resistor the charge is neutralised and so the current falls
• rate of decrease of p.d. also falls

Question 15

What is the equation for the fractional drop in charge during the discharging process?

Answer 15

delta Q/ Q = - delta t/CR

Question 16

What is the equation for the exponential decrease in charge with respect to time for discharging?

Answer 16

Q = Qo e^-t/RC

Question 17

What does the gradient of the tangent to the curve at a point on a Q-t graph give?

Answer 17

The current at that time

Question 18

On a current-time graph, what does the area underneath the curve give?

Answer 18

Charge stored

Question 19

What is the time constant of a circuit?

Answer 19

RC

where R = resistance of circuit and C = capacitance

At time t = RC after the start of the discharge, the charge falls to 0.37 (e^-1) of it’s initial value

unit: seconds (s)

Question 20

When t=2RC in a capacitor’s discharge, what percentage charge remains?

Answer 20

14%

Question 21

At what point, is a capacitor considered discharged?

Answer 21

When t=5RC

Question 22

When is a capacitor fully discharged?

Answer 22

When the charge on the plates is zero and the current and p.d. are also zero

Question 23

How do you know when a capacitor is fully charged?

Answer 23

Pd is equal to the source pd

Current is zero because no more charge flows in the circuit

Question 24

Draw a charging curve for a capacitor through a fixed resistor for charge against time

Answer 24

Question 25

How can you increase the charge stored on a capacitor?

Answer 25

Inserting a dielectric between the plates

Question 26

What are dielectrics?

Answer 26

Electrically insulating materials materials that increase the ability of a parallel plates to store charge

Increase charge stored in a capacitor for any given pd. So increases capacitance of capacitor

Question 27

How does a dielectric increase the charge stored in a capacitor?

Answer 27

When a dielectric is placed between two oppositely charged parallel plates connected to a battery, each molecule in the dielectric becomes polarised (electrons pulled slightly towards the positive plate). Surface of dielectric facing the positive plate gains a negative charge As a result more charge is stored as:

• positive side of dielectric attracts more electrons from the battery onto the negative plate
• negative side of the dielectric pushes electrons back tot eh battery from the positive plate

Question 28

What is the relative permittivity of a dielectric substance?

Answer 28

Ratio of charge stored with the dielctric susbstance t the charge stored without

Er = Q/Qo

where Qo is the charge stored at the same pd when the space is completely empty.

Question 29

What is the relative permittivity of a substance also called?

Answer 29

dielectric constant

Question 30

What is the equation for capacitance of a capcitor with a dielectric

Answer 30

C = AEoEr/d

where A is the surface area of each plate and d = spacing between the plates

Question 31

What can large capacitance be achieved by?

Answer 31

• Making the area A as large as possible
• Making the plate spacing d as small as possible
• filling the space between the plates with a dielectric which has a relative permittivity as large as possible

Question 32

Why do most capacitors consist of two strips of aluminium foil seperated by a layer of dielectric?

Answer 32

Makes capacitance as large as possible because area A is as large as possible and the spacing d is as small as possible.

Question 33

Describe the procedure for measuring the relative permittivity of a dielectric substance

Answer 33

Place dielectric sheets of uniform thickness between two parallel plates insulated from each other by small pieces of suitable insulation. A potential divider is used to apply a constant pd between the two plates. The capcitor is repeatedly charged and discharged through a microammeter. The microammeter current reading is proportional to the charge gained by the capacitor each time the the switch charges it. The current is measured with the dielectric in place and with the dielectric replaced by small insulating spacers of the same thickness as the dielectric sheet . Relative permittivity of the dielectric = I/Io where I is the current with the dielectric present

Question 34

Draw the circuit used in measuring the relative permittivity of a dielectric substance?

Answer 34

Question 35

When does dielectric polarisation occur?

Answer 35

When a dielectric is placed in an electric field and the electric charges shift from the average equilibrium positions

Question 36

What is the effect of dielectric polarisation?

Answer 36

• +ve charges are displaced toward field and -ve shift in opposite direction
• creates internal electric field that reduces overall field within dielectric so reducing p.d. across capacitor

Question 37

What is the effect of an internal electric field in a dielectric?

Answer 37

It reduces the overall field within the dielectric itself, reducing the p.d. across the capacitor

Question 38

How can the p.d. return to its original value after dielectric polarisation?

Answer 38

Requires the addition of more charge onto the plates

Question 39

What effect does dielectric polarisation have on the capacitor overall?

Answer 39

The capacitor can store more charge for the same p.d. and increase its capacitance