Capacitance

Question 1

Explain what is meant by the capacitance of an object.

Answer 1

The amount of charge it is able to store per unit potential difference across it.

Question 2

Describe the structure of a capacitor.

Answer 2

Two electrical conducting plates.
Separated by an insulator known as a dielectric.

Question 3

What determines the voltage a capacitor will charge up to?

Answer 3

A capacitor will only charge up to the voltage of the cell or battery charging it.

Question 4

Why do capacitors have a voltage rating?

Answer 4

This is the maximum potential difference that can be safely put across it.

Question 5

What does a Q-V graph look like for a capacitor and what does the gradient represent and the area underneath represent?

Answer 5

Gradient = capactitance
Area = (electrical potential) energy stored

Question 6

Why is energy stored by a capacitor?

Answer 6

Work has to be done to push electrons onto the negative plate and to remove electrons from the positive plate.

Question 7

What does permittivity mean?

Answer 7

Measure of how difficult it is to generate an electric field in a certain material.
Higher value = more difficult = weaker field strength for a given charge.

Question 8

What is ε_r?

Answer 8

Relative permittivity (or dielectric constant)
Ratio of the permittivity of a material to the permittivity of free space.
Has no units.

Question 9

How can ε_r be calculated for a material?

Answer 9

ε_r = ε₁ / ε₀

Question 10

Describe the molecules in a dielectric.

Answer 10

They are polar molecules.
So have a positive end and a negative end.

Question 11

Describe the orientation of the dielectric molecules when no charge is stored by the capacitor.

Answer 11

Molecules are aligned randomly.

Question 12

Describe and explain the orientation of the dielectric molecules when charge is stored by the capacitor.

Answer 12

An electric field is generated across the dielectric.
Negative ends of molecules attracted to the positively charged plate and vice versa.
Molecules rotate and align with electric field.

Question 13

Explain the effect that the dielectric molecules have on the overall electric field.

Answer 13

The dielectric molecules each have their own electric field.
Which opposes the electric field of the capacitor.
Causing the overall field to be reduced.

Question 14

How does the permittivity of the dielectric affect the overall field?

Answer 14

Larger permittivity of the dielectric = larger opposing field.
Greater reduction in overall field.

Question 15

Explain the effect this has on the capacitance of the capacitor.

Answer 15

Overall electric field E reduces and E = V/d, so this reduces the p.d. needed for a given charge.
As C = Q/V, the capacitance increases.

Question 16

If a change is made to a capacitor whilst still connected to the battery, what happens?

Answer 16

Voltage across it must stay the same.
Capacitance changes, which causes charge stored to change.

Question 17

If a capacitor is disconnected from a battery and a change is made to it, what happens?

Answer 17

Charge stored must stay the same.
Capacitance changes, which causes voltage across it to change.

Question 18

Explain, in terms of electrons, what happens when a capacitor is charged.

Answer 18

Electrons are repelled by the negative terminal and build up on one plate making it negative.
Electrons are also attracted to the positive terminal and removed from the other plate making it positive.
Plates gain an equal and opposite charge.
No electrons flow directly between plates due to insulation.

Question 19

Describe the energy transfers that take place when charging through a fixed resistor.

Answer 19

Chemical energy in battery is transferred to electrical potential energy in the capacitor and to thermal energy in the resistor which is dissipated to the surroundings.
(Half the energy to the capacitor, half to the resistor).

Question 20

When charging through a fixed resistor, sketch a graph to show how current changes over time and give the equation. What does the area under the graph represent?

Answer 20

Graph of I = I₀e^{-t / RC}
Area under graph = charge stored.

Question 21

How can the initial current I₀ be determined?

Answer 21

Applying Kirchoff’s voltage law: 𝜀 = 𝑉_𝑅 + 𝑉_𝐶
Which gives: 𝜀 = 𝐼𝑅 + 𝑄/𝐶
Initially Q = 0, so this gives 𝐼_𝑜 = 𝜀 / 𝑅

Question 22

When charging through a fixed resistor, sketch a graph to show how potential difference changes over time and give the equation.

Answer 22

V = V₀(1 - e^{-t / RC})

Question 23

When charging through a fixed resistor, sketch a graph to show how charge changes over time and give the equation. What does the gradient of the graph represent?

Answer 23

Q = Q₀(1 - e^{-t / RC})
Gradient = current

Question 24

Define time constant (RC) in terms of current, potential difference and charge when charging through a fixed resistor.

Answer 24

Time for the current to decrease to (1 / e) or 37% of its original value.
Time for potential difference or charge to increase to 1 − (1 / e) or 63% of its final value.

Question 25

Give a reasonable estimate for the time taken to charge a capacitor.

Answer 25

5 time constants (5RC).

Question 26

Define half-life (T_1/2) in terms of the current when charging through a fixed resistor.

Answer 26

Time taken for the current to halve.

Question 27

Give the equation that relates half-life (T_1/2) to the time constant (RC).

Answer 27

T_1/2 = ln2 x RC = 0.69 RC

Question 28

Explain, in terms of electrons, what happens when a capacitor is discharged through a fixed resistor.

Answer 28

Electrons flow from the negative plate to the positive plate.
Capacitor loses charge.

Question 29

Describe the energy transfers that take place when charging through a fixed resistor.

Answer 29

Electric potential energy stored by the capacitor is trasnferred to the thermal energy of the resistor which is dissipated to the surroundings.

Question 30

When discharging through a fixed resistor, sketch a graph to show how current changes over time and give the equation. What does the area under the graph represent?

Answer 30

I = I₀e^{-t / RC}
Area under graph = charge removed.

Question 31

How can the initial current I₀ be determined?

Answer 31

Applying Kirchoff’s voltage law: 𝑉_𝐶 = 𝑉_𝑅
Which gives: 𝑉_C = 𝐼𝑅
Initially 𝑉_C = 𝑉₀ = 𝜀, so this gives 𝐼₀ = 𝜀 / 𝑅
Where 𝜀 is the emf of the charging cell or battery.

Question 32

When discharging through a fixed resistor, sketch a graph to show how potential difference changes over time and give the equation.

Answer 32

V = V₀e^{-t / RC}

Question 33

When discharging through a fixed resistor, sketch a graph to show how charge changes over time and give the equation. What does the gradient of the graph represent?

Answer 33

Q = Q₀e^{-t / RC}
Gradient = current.

Question 34

Define time constant (RC) in terms of current, potential difference and charge when discharging through a fixed resistor.

Answer 34

• Time for the current, potential difference or charge to decrease to (1 / e) or 37% of its original value.

Question 35

Give a reasonable estimate for the time taken to discharge a capacitor.

Answer 35

5 time constants (5RC).

Question 36

Define half-life (T_1/2) in terms of the current, potential difference and charge when discharging through a fixed resistor.

Answer 36

Time taken for the current, potential difference or charge to halve.

Question 37

Give the equation that relates half-life (T_{1/2) to the time constant (RC).}

Answer 37

T_{1/2 = ln2 x RC = 0.69 RC}