4.1 Capacitance

Question 1

What is the structure of a simple parallel-plate capacitor?

Answer 1

Two equal metal plates placed parallel to one another, with either air or a vacuum between them.

Question 2

How does a capacitor store energy?

Answer 2

Work is done in transferring charge from one plate to the other, which becomes potential energy stored in the capacitor.

Question 3

What is capacitance?

Answer 3

The capacitance, C, is the charge stored, Q, per unit potential difference, V, across the two plates. Therefore we have C = Q / V. It is measured in Farads, F (1F = 1CV-1).

Question 4

How can capacitance be increased?

Answer 4

● By adding an insulator between the plates, called a dielectric.
● The dielectric reduces the strength of the electric field, decreasing the voltage.
● Since voltage and capacitance are inversely proportional, capacitance increases.

Question 5

What is the shape of the electric field between the plates?

Answer 5

The field is uniform, so the field lines are parallel and evenly spaced, pointing from positive to negative.

Question 6

What is the formula for the electric field strength between the plates?

Answer 6

Field strength (V m-1) = potential difference (V) / distance between the plates (m)
E =V / d

Question 7

What is the formula for the capacitance of a parallel-plate capacitor with no dielectric?

Answer 7

C = Aε0 / d
C = capacitance (F), A = area of plates (m2), ε = permittivity of free space (8.85 x 10^-12),
d = distance between the plates (m)

Question 8

What is the equation for the total capacitance in series?

Answer 8

Question 9

What is the equation for the total capacitance in parallel?

Answer 9

Question 10

What is the formula for the energy stored in a capacitor?

Answer 10

Energy stored = 0.5QV

Question 11

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

Answer 11

The energy stored by the capacitor.

Question 12

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

Answer 12

Question 13

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

Answer 13

Question 14

Describe the I against t graph for the discharging of a capacitor through a resistor.

Answer 14

Question 15

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

Answer 15

Question 16

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

Answer 16

Question 17

What is the time constant?

Answer 17

Question 18

How was 37% derived when using the time constant?

Answer 18

● Start with the formula Q = Q0e-t/RC.
● When t = RC (after 1 time constant), the formula becomes Q = Q0e-1.
● e-1 ≈ 0.37, which is where 37% came from.

Question 19

What equations do we require for charging a capacitor?

Answer 19

Charging up a capacitor produces Q = Q0(1 - e-t/RC) &
V = V0(1 - e-t/RC) where V0 is the battery PD and Q0=CV0.

Question 20

How does a capacitor charge up?

Answer 20

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 positive 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 current stops flowing.

Question 21

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

Answer 21

1. Electrons move in opposite direction than when the capacitor was charging up.
2. Charge on plate A decreases as it loses electrons, and plate B gains electrons, so A and B become neutral.
3. P.d. decreases exponentially across the plates.

Question 22

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

Answer 22

1. 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.
2. 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.