6.1 - Capacitors

Question 1

What is a capacitor?

Answer 1

• A capacitor is an electrical component that stores charge on 2 separate metallic plates.
• An insulator, called a dielectric, is placed between the plates to prevent the charge from travelling across the gap.

Question 2

What is capacitance?

Answer 2

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 3

What is the relative permittivity (a.k.a. dielectric constant)?

Answer 3

• 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 4

What is the equation for the total capacitance in series?

Answer 4

1/Cₜₒₜₐₗ = 1/C₁ + 1/C₂ + …

Question 5

What is the equation for the total capacitance in parallel?

Answer 5

Cₜₒₜₐₗ = C₁+ C₂+ …

Question 6

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

Answer 6

The energy stored by the capacitor.

Question 7

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

Answer 7

Qₜ = Q₀ e⁻ᵗ/ᴿᶜ

Question 8

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

Answer 8

V꜀ = V(bat) e⁻ᵗ/ᴿᶜ

Question 9

Describe the I against t graph for the discharging/charging of a capacitor through a resistor with equation

For current charging and discharging has the same graph and equation

Answer 9

Iₜ = I₀ e⁻ᵗ/ᴿᶜ

Question 10

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

Answer 10

Qₜ = Q₀ (1 - e⁻ᵗ/ᴿᶜ)

Question 11

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

Answer 11

V꜀ = V(bat) (1 - e⁻ᵗ/ᴿᶜ)

Question 12

What is the time constant?

Answer 12

The time it takes for the charge in a capacitor falls to 37% of the initial value (explained in the following slide) given by RC (resistance x capacitance).
A capacitor is considered fully discharged after 5 time constants.

Question 13

How was 37% derived when using the time constant?

Answer 13

• 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 14

What is the half time of a capacitor?

Answer 14

T½ = 0.69RC

Question 15

What equations do we require for charging a capacitor?

Answer 15

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 16

How does a capacitor charge up?

Answer 16

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 17

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 17

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

Question 18

State some uses of capacitors.

Answer 18

• Flash photography
• Nuclear fusion
• Backup power supplies
  Also:
• DC blocking
• Smoothing AC to DC
• Tuning (Resonating magnetic field)

Question 19

State the 3 expressions for the energy stored by a capacitor.

Answer 19

E = ½ (Q²/C) = ½ (QV) = ½ (CV²)

Question 20

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

Answer 20

• 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 21

Equation for capacitance that includes factors that affect it

Answer 21

C = εA/D

C - Capacitance (F)
ε - Electricial permitivity of dielectric (Fm⁻¹)
A - Area (m²)
D - Separation of capacitor plates (m)