Section 10 - Capacitors

Question 1

What is the relative permittivity (aka dielectric constant)?

Answer 1

• The ratio of the charge stored with the dielectric between the plates to the charge stored when the dielectric is not present
• εr = Q/Q0
• The greater the relative permittivity, the greater the capacitance of the capacitor

Question 2

What is the mark scheme definition of the dielectric constant?

Answer 2

permittivity of medium/permittivity of free space

Question 3

How does the dielectric constant affect capacitance?

Answer 3

With a dielectric, the capacitance of the capacitor is multiplied by the dielectric constant

Question 4

What does the area under the graph of charge against pd represent?

Answer 4

The energy stored by the capacitor

Question 5

Describe the Q against t graph for the discharging of a capcitor through a resistor

Answer 5

A graph that looks like a half life graph, the graph hits the y axis

Question 6

Describe the V agaisnt t graph for the discharging of a capacitor through a resistor

Answer 6

A graph that looks like a half life graph, the graph hits the y axis

Question 7

Describe the I agaisnt t graph for the discharging and charging of a capacitor through a resistor

Answer 7

A graph that looks like a half life graph, the graph hits the y axis

Question 8

Describe the Q against t graph for the charging of a capacitor through a fixed resistor

Answer 8

An upside down half life graph that meets the origin

Question 9

Describe the V agaisnt t graph for the charging of a capacitor through a fixed resistor

Answer 9

An upside down half life graph that meets the origin

Question 10

What is the time constant?

Answer 10

The time it takes for the charge in a capacitor to fall to 37% of the initial value given by RC - a capacitor is considered fully discharged after 5 time constants

Question 11

How was 37% derived when using the time constant?

Answer 11

• Start with the formula Q = Q0e^-t/RC
• When t=RC (after 1 time constant), the formula becomes Q=Q0e^-1
• e^-1 is approximately 0.37

Question 12

What is the half time of a capacitor?

Answer 12

T1/2 = 0.69RC

Question 13

What equations do we require for charging a capacitor?

Answer 13

Q=Q0(1-e^-t/RC)
V=V0(1-e^-t/RC)
V0 is the battery PD and Q0=CV0

Question 14

How does a capacitor charge up?

Answer 14

1. Electrons move from negative to positive around the circuit
2. The electrons are deposited on plate A, making it negatively charged
3. Electrons travel from plate B to the positive terminal of the battery, giving the plate a postitive charge
4. Electrons build up on plate A and an equal amount of electrons are removed from plate B, creating a potential difference across the plates
5. When the p.d. across plates = source p.d., the capacitor is fully charged and the current stops flowing

Question 15

Describe and explain in terms of the movement of electrons how the p.d across a capacitor changed, when it discharges across a resistor

Answer 15

1. Electrons move in opposite direction than when the capacitor was charging up
2. Charge on one plate decreases as it loses electrons and the other plate gains elecrons, neutralising them
3. P.d decreases exponentially across the plates

Question 16

State the 3 expressions for the energy stored by a capacitor

Answer 16

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

Question 17

What 2 factors affect the time taken for a capacitor to charge or discharge?

Answer 17

• The capacitance of the capacitor, C - this affects the amount of charge that can be stored by the capacitors at any given potential difference across it
• The resistance of the circuit, R - this affects the current in the circuit and how quickly it flows, hence how quickly the capacitor charges/discharges

Question 18

How does inserting a charged dielectric change the capacitance?

Answer 18

1. The dielectric aligns with their positive side facing the capacitor’s plates negative side
2. This produces a counter electric field
3. The p.d. reduces between the capacitor plates, but the charge stays the same
4. C=Q/V therefore capacitance increases

Question 19

What is the energy difference equation?

Answer 19

E=1/2Q^2 (1/c2-1/c1)

Question 20

If the same maximum capicitance is required using plates with half the diameter, what are 2 ways to acheive this? Include numerical data

Answer 20

1. Insert a dielectric with a relative permittivity of 4
2. Reduce the air gap by 1/4

Question 21

How do you draw a dc supply oscilloscope with the same rate of energy dissipation as an ac.

Answer 21

Draw a sraight horizontal line at the Vrms

Question 22

How do you find the frequency from an oscilloscope?

Answer 22

T = Number of divisions across the whole wave x time per division
f=1/T

Question 23

State and explain a change to one control setting on the oscilloscope that would reduce the uncertainty in the value of the time constant

Answer 23

• Reduce the time base setting
• Uncertainty is due to the smallness of the divisions and this means the waveform will be stretched horizontally

Question 24

What is the use of a mirror when doing an analogue reading?

Answer 24

• Move position until the needle is aligned with its reflection in the mirror
• Reduces parallax error