Capacitors

Question 1

What do capacitors do?

Answer 1

Capacitors build up charge on plates

Question 2

What is a capacitor?

Answer 2

A capacitor is an electrical component made up of two conducting plates separated by a gap or a dielectric (an insulating material)

Question 3

What happens when a capacitor is connected to a power source?

Answer 3

When a capacitor is connected to a power source, positive and negative charge build up on opposite plates creating a uniform electric field between them

Question 4

Define capacitance

Answer 4

The capacitance of a capacitor is the amount of charge per unit potential difference stored by the capacitor between its plates

Question 5

State the formula used to calculate the capacitance of a capacitor

Answer 5

C = Q/V
- Q is the charge in coulombs
- V is the potential difference in volts
- C is the capacitance in Farads

Question 6

What are the base units for a farad?

Answer 6

1 farad = 1 Coulomb per volt

Question 7

Explain the size of the farad and hence the general metrics capacitances are expressed in

Answer 7

A farad is a huge unit so capacitances will be usually expressed in microfarads, nanofarads and picofarads

Question 8

Sketch a general diagram of a parallel plate capacitor

Answer 8

See page 132 in the revision guide

Question 9

What effect can dielectrics be used for in capacitors?

Answer 9

You can increase capacitance using dielectrics

Question 10

Define permittivity

Answer 10

Permittivity is a measure of how difficult it is to generate an electric field in a certain material

Question 11

Define relative permittivity

Answer 11

The relative permittivity is the ratio of the permittivity of a material to the permittivity of free space

Question 12

State the formula used to calculate relative permittivity

Answer 12

εr= ε1/ε0
- εr is the relative permittivity of matrerial 1
- ε1 is the permittivity of material 1 in farads per metre
- ε0 is the permittivity of free space

Question 13

What is relative permittivity sometimes also called?

Answer 13

Relative permittivity is sometimes also called the dielectric constant

Question 14

Explain what is happening in a capacitor when there is no charge applied to it

Answer 14

• The dielectric in the capacitor is made up of lots of polar molecules, these polar molecules have a positive end and a negative end
• When no charge is stored by the capacitor there is no electric field so these molecules point in a bunch of random directions

Question 15

Explain what is happening in a capacitor when a charge is applied to it

Answer 15

• When a charge is applied to a capacitor an electric field is generated
• The negative ends of the molecules are attracted to the positively charged plate and vice versa
• This causes all of the molecules to rotate and align themselves with the electric field
• The molecules each have their own electric field which in this alignment now opposes the applied electric field of the capacitor. The larger the permittivity, the larger this opposing field is
• This reduces the overall electric field which reduces the potential difference needed to charge the capacitor so the capacitance increases

Question 16

State the formula used to calculate the capacitance of a capacitor using its dimensions

Answer 16

C = Aε0εr / d
- A is the area of the plates in m^2
- ε0 is the permittivity of free space in F/m
- εr is the relative permittivity of the dielectric
- d is the separation of the plates in m

Question 17

What is the relationship between capacitors and energy?

Answer 17

Capacitors store energy

Question 18

What happens when charge builds up on the plates of a capacitor?

Answer 18

When charge builds up on the plates of a capacitor, electrical energy is stored by the capacitor

Question 19

How can you find the energy stored in a capacitor from a graph of charge stored against potential difference

Answer 19

You can find the energy stored in a capacitor from the area under a graph of charge stored against potential difference

Question 20

Describe the graph of charge stored against potential difference for a capacitor

Answer 20

The potential difference across the capacitor is directly proportional to the charge stored in it so the graph will be a straight line through the origin

Question 21

What does the gradient of a graph of charge stored against potential difference for a capacitor give?

Answer 21

The gradient is equal to the capacitance of the capacitor

Question 22

State the three formulas used to calculate the energy stored by a capacitor

Answer 22

E = 1/2QV = 1/2CV^2 = 1/2Q^2/C

Question 23

Explain the method for the practical for investigating what happens when you charge a capacitor

Answer 23

• Set up the test circuit (see page 134 in revision guide)
• Close the switch to connect the uncharged capacitor to the dc power supply
• Let the capacitor charge whilst the data logger records both the potential difference (from the voltmeter) and the current (from the ammeter) over time
• When the current through the ammeter is zero the capacitor is fully charged

Question 24

What graphs can you plot using the results from the investigating what happens when you charge a capacitor practical?

Answer 24

You can plot graphs of current, potential difference and charge against time

Question 25

Plot the three graphs of current, potential difference and charge against time using the results from the charging a capacitor practical

Answer 25

See page 134 in the revision guide

Question 26

Explain what happens once the capacitor begins charging in the charging a capacitor practical

Answer 26

1- As soon as the switch closes, current starts to flow. The electrons flow onto the plate connected to the negative terminal of the dc power supply so a negative charge builds up
2- This build-up of negative charge repels electrons off the plate connected to the positive terminal of the power supply making that plate positive. These electrons are attracted to the positive terminal of the power supply
3- An equal but opposite charge builds up on each plate causing a potential difference between the plates. No charge can flow between the plates because they are separated by an insulator
4- As charge builds up on the plates, electrostatic repulsion makes it harder and harder for more electrons to be deposited. When the potential difference across the capacitor is equal to the potential difference across the power supply the current falls to zero

Question 27

Explain the method for discharging the capacitor in the charging a capacitor practical

Answer 27

1- To discharge the capacitor, remove the power supply from the test circuit and close the switch to complete the circuit
2- Let the capacitor discharge whilst the data logger records potential difference and current over time
3- When the current through the ammeter and the potential difference across the plates are zero, the capacitor is fully charged

Question 28

Plot the three graphs of current, potential difference and charge against time for the capacitor discharging in the charging a capacitor practical

Answer 28

See page 135 in the revision guide

Question 29

Explain what is happening when the capacitor is discharging in the charging a capacitor practical

Answer 29

1- The current flows in the opposite direction from the charging current
2- As the potential difference decreases, the current decreases as well
3- When a capacitor is discharging, the amount of charge on and potential difference between the plates falls exponentially with time. That means it always takes the same length of time for the charge or potential difference to halve no matter what value it starts at
4- The same is true for the amount of current flowing around the circuit

Question 30

What two factors affects the time taken to charge or discharge a capacitor?

Answer 30

The time it takes to charge or discharge a capacitor depends on:
1- The capacitance of the capacitor (C). This affects the amount of charge that can be transferred at a given potential difference
2- The resistance of the circuit (R). This affects the current in the circuit

Question 31

What type of growth does the charge on and the potential difference across the plates in a capacitor show as it is charged?

Answer 31

When a capacitor is charging the growth rate of the amount of charge on and potential difference across the plates shows exponential decay (so over time they increase more and more slowly)

Question 32

State the formula for calculating the charge on the plates of a capacitor at a given time after beginning charging

Answer 32

Q = Q0(1-e^-t/RC)
- Q0 is the charge of the capacitor when it is fully charged
- t is the time since charging began in seconds
- R is the resistance
- C is the capacitance

Question 33

State the formula for calculating the potential difference between the plates of a capacitor at a given time after beginning charging

Answer 33

V = V0(1-e^-t/RC)
- V0 is the initial potential difference across the plates of the capacitor
- t is the time since charging began in seconds
- R is the resistance
- C is the capacitance

Question 34

State the formula for calculating the charging current on a capacitor at a given time

Answer 34

I = I0e^-t/RC
- Io is the initial charging current on the capacitor
- t is the time since charging began in seconds
- R is the resistance
- C is the capacitance

Question 35

State the formula for calculating the charge left on the plates of a capacitor after it begins discharging from being fully charged

Answer 35

Q = Q0e^-t/RC

Question 36

State the formula for calculating the potential difference across the plates of a capacitor after it begins discharging from being fully charged

Answer 36

V = V0e^-t/RC

Question 37

State the formula for calculating the discharging current of a capacitor after it begins discharging from being fully charged

Answer 37

I = I0e^-t/RC

Question 38

Why is the formula for the charging and discharging current of a capacitor the same?

Answer 38

The formula is the same as the current just travels in the opposite direction of the charging current

Question 39

State the formula used to calculate the time constant of a capacitor

Answer 39

𝜏 = RC

Question 40

What is the time constant of a capacitor?

Answer 40

The time constant (𝜏) is the time taken for the charge or potential difference or current of a discharging capacitor to fall to 37% of its value when fully charged. Its also the time taken for the charge or potential difference of a charging capacitor to rise to 63% of its value when fully charged

Question 41

The larger the resistance in series with the capacitor….

Answer 41

the longer it takes to charge or discharge

Question 42

In practice what is the general time taken for a capacitor to charge or discharge fully?

Answer 42

5𝜏 = 5RC

Question 43

Reduce the equation for the charge on a discharging capacitor into the form y=mx+c using natural logs

Answer 43

See page 137 in the revision guide
- The gradient of the graph of lnQ against t would be -1/RC = -1/𝜏
- The y-intercept would be lnQ0

Question 44

What is the time to halve for a capacitor?

Answer 44

The time to halve is the time taken for the charge, current or potential difference of a discharging capacitor to reach half of the value it was when it was fully charged

Question 45

State the formula used to calculate the time to halve for a capacitor

Answer 45

T1/2 = 0.69RC