6.1 Capacitors

Question 1

What is the function of a capacitor

Answer 1

Electrical devices that store charge, creating a build up of potential difference

Question 2

What is a capacitor (physically)

Answer 2

Two metal plates with a dielectric between them
They only store charge when the plates overlap

Question 3

What is capacitance and state its units

Answer 3

The charge stored per unit potential difference

Farads (F)

Question 4

What is the equation for capacitance

Answer 4

Capacitance (F) = Charge (C) / Potential difference (V)

C = Q/V

Question 5

What are the uses of capacitors

Answer 5

Cameras - flash photography
Electronic timing circuits
Power supply back up in power cuts
Power devices with memory store

Question 6

How do capacitors get charged up

Answer 6

Negative terminal repels electrons
They travel to the capacitor plate on that side
The plate becomes negatively charged

The electrons are attracted to the positive terminal
They leave the capacitor plate on that side
The plate becomes positively charged

Question 7

Why does the rate of charging up slow down

Answer 7

Electrons already of the plate repel new ones (electrostatic repulsion)

Question 8

Describe the V/t, I/t, and Q/t graphs for charging up a capacitor

Answer 8

V/t and Q/t graphs increase rapidly and then the rate decreases and the graph plateaus

I/t graph shows exponential decay but starts on the y axis

Question 9

What are the equations associated with charging up a capacitor

Answer 9

Pd = final pd(1 - e^{-time /ResistancexCapacitance})

V = V_f (1-e^^-t/RC)

Charge = final charge (1 - e^{-time /ResistancexCapacitance})

Q = Q_f (1-e^^-t/RC)

Current = initial current(1 - e^{-time /ResistancexCapacitance})

I = I₀ (1-e^^-t/RC)

Question 10

How do capacitors discharge

Answer 10

When no power supply is present the electrons from the negative to the positive plate until they are balanced and pd is zero

Question 11

Describe the V/t, I/t, and Q/t graphs for charging up a capacitor

Answer 11

All three graphs show exponential decay

Question 12

What are the equations associated with discharging a capacitor

Answer 12

Charge = initial charge x e^{time/ ResistancexCapacitance}

Q = Q₀e^-t/RC

Current = initial current x e^{time/ ResistancexCapacitance}

I = I₀e^-t/RC

Pd = initial pd x e^{time/ ResistancexCapacitance}

V = V₀e^-t/RC

Question 13

What is the time constant for charging/discharging a capacitor

Answer 13

The time taken (s) to decrease the value of charge/pd/current by 1/e

𝜏 = RC

Question 14

What is the rule for capacitors in series

Answer 14

The pd is shared and charge is constant
So total capacitance shared too

V is inversely proportional to C

1/C_T = 1/C₁ + 1/C₂ …

Question 15

What’s the rule for capacitance in parallel

Answer 15

The pd is constant and the charge is shared
So capacitance is shared too

Q is directly proportional to C

C_T = C₁ + C₂ …

Question 16

What does the area under a current-time (I/t) graph show

Answer 16

Q=It

Therefore the area is equal to the charge

Question 17

What does the gradient on a pd-charge (V/Q) graph show

Answer 17

V = Q/C

Therefore gradient is 1/C

Question 18

What does the area under a pd-charge (V/Q) graph show and explain the relationship

Answer 18

Work done (J)

W=0.5VQ (as it’s a directly proportional relationship between V and Q the rea is a triangle hence 0.5)

Work is done on the electrons to move them to the plates during charging
As the charge of the negative plate increases more work must be done to overcome electrostatic repulsion5

Question 19

What are the equations for energy stored on a capacitor

Answer 19

Work done (J) = 1/2 x charge (C) x pd (V)

W=0.5QV

Work done (J) = 1/2x capacitance (F) x pd² (V)

W = 0.5CV²

Work done (J) = charge² / 2xCapacitance (F)

W = 0.5Q²/C

Question 20

How is relative permittivity affected by electric fields in a dielectric

Answer 20

Polar molecules in the dielectric create an opposing field to that of the capacitors plates
The larger this field is, the larger the permittivity

Question 21

How does the dielectric affect the electric field of a capacitor

Answer 21

The opposing field from the polar molecules in the dielectric decreases the overall field
This decreases the pd, therefore increasing capacitance

Question 22

How to calculate capacitance from permittivity

Answer 22

Capacitance (F) = area (m) x relative permittivity (Fm^-) x ermittivity of free space (Fm^-1) / separation of plates (m)

C = Aε^rε⁰/d

Question 23

What is a spherical conductor

Answer 23

A type of capacitor where charge builds on the surface

Question 24

What is the capacitance of an isolated sphere

Answer 24

Combine V = Q/ 4πε₀r where r=R, radius of the sphere
and V = Q/C

To get C = 4πε₀R