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

Answer 2

The energy stored by the capacitor

Question 3

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

Answer 3

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

Question 4

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

Answer 4

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

Question 5

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

Answer 5

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

Question 6

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

Answer 6

An upside down half life graph that meets the origin

Question 7

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

Answer 7

An upside down half life graph that meets the origin

Question 8

What is the time constant?

Answer 8

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 9

How was 37% derived when using the time constant?

Answer 9

• 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 10

What is the half time of a capacitor?

Answer 10

T1/2 = 0.69RC

Question 11

What equations do we require for charging a capacitor?

Answer 11

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

Question 12

How does a capacitor charge up?

Answer 12

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 13

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 13

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 14

State the 3 expressions for the energy stored by a capacitor

Answer 14

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

Question 15

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

Answer 15

• 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 curretn in the circuit and how quickly it flows, hence how quickly the capacitor charges/discharges

Question 16

How does inserting a charged dielectric change the capacitance?

Answer 16

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