Capacitance

Question 1

Define Capacitance

Answer 1

The charge stored (Q) by a capacitor per unit potential difference

Question 2

How does a capacitor cause a uniform electric field

Answer 2

When 2 parallel metal plates are connected to a battery, (-ve) electrons from the battery go to one plate, making it (-ve) Then electrons leave the other plate and go to the battery making that plate (+ve) Opposite charges building up on the 2 parallel plates cause the field between them

Question 3

What is a capacitor

Answer 3

An electrical component that stores charge Made up of 2 conducting parallel plates with a gap in between that may have a dielectric in

Question 4

What is a dielectric

Answer 4

An insulating material that can be put between 2 conducting parallel plates to increase the ability of the capacitor to store charge

Question 5

Define permittivity

Answer 5

Measure of the ability to store an electric field in the material

Question 6

What does it mean for a capacitor to store charge

Answer 6

One conductor stores charge Q+ (Electrons that left it to go to the battery) and one conductor stores charge Q- (Electrons that came to it from the battery)

Question 7

How does a dielectric increase the ability of a capacitor to store charge

Answer 7

When placed between the 2 plates, molecules in the dielectric become polarised.

So the side facing the positive plate becomes negatively charged, repelling more electrons from the positive plate, making it more positively charged.

The side facing the negative plate becomes positively charged, attracting more electrons to the negative plate, making it more negatively charged

Question 8

What does it mean for molecules in a dielectric to become polarised

Answer 8

Dielectrics have polar molecules - one side positive, one side negative.

In no electric field, they are arranged in random directions

But in an electric field, they align themselves with the field

Question 9

What is relative Permittivity Σ_r

How do you calculate it

Answer 9

Ratio of charged stored with the dielectric to charge stored without the dielectric

Q/Q₀

Q₀ - Charge stored without dielectric

OR

C/C₀

C₀ - Capacitance without dielectric

OR

Ratio of permittivity of dielectric to permittivity of free space

Σ_r=Σ/Σ₀

Question 10

How to calculate the capacitance of a capacitor with a dielectric in it

Answer 10

C = (Aε_r ε₀ )/d

ε_r ε₀ = Permittivity of dielectric

Question 11

How can one increase the capacitance of a capacitor that has a dielectric

Answer 11

Making the area of each plate larger

Decreasing the spacing of plates

Filling space with a dielectric with a large permittivty

Question 12

What does a µ represent

Answer 12

x10^-6

Question 13

Why does a capacitor store energy

What form is this energy stored as

Answer 13

As work is done to force electrons onto 1 plate and off the other

Electric Potential Energy

Question 14

How does potential difference across a capacitor change with charge stored

Answer 14

As potential difference is the energy per coulomb

P.d across a capacitor increases proportionally to the charge stored

Question 15

What does the area under a Q-V graph represent

Answer 15

Energy stored in a capacitor

Question 16

How to charge a capacitor

Answer 16

Connect it in a circuit with a power supply and resistor

Question 17

I-t graph for a charging capacitor and its equation

Answer 17

I=I₀e^-(t/RC)

Question 18

V-t graph for a charging capacitor and its equation

Answer 18

V=V₀(1-e^-(t/RC))

Question 19

Q-t graph for a charging capacitor and its equation

What does the gradient represent

Answer 19

Current

Q=Q₀(1-e^-(t/RC))

Question 20

Describe what happens when a capacitor is charging up

Answer 20

Current starts to flow and negative charge builds up on the plate connected to the negative terminal. of the cell.

On the opposite plate, electrons are repelled by the negative charge building up on the other (now increasing negative) plate

Therefore these electrons move to the positive terminal of the cell and an equal but opposite charge is formed on each plate, creating a potential difference.

As the charge across the plates increases, the potential difference increases but the electron flow decreases due to the force of electrostatic repulsion also increasing, therefore current decreases and eventually reaches zero.

Question 21

How do you discharge a capacitor

Answer 21

Connect it to a closed circuit with just a resistor

Question 22

I-t graph for a discharging capacitor and its equation

Answer 22

I=I₀e^-(t/RC)

Question 23

V-t graph for a discharging capacitor and its equation

Answer 23

V=V₀e^-(t/RC)

Question 24

Q-t graph for a discharging capacitor

Answer 24

Q=Q₀e^-(t/RC)

Question 25

Why does current gradually decrease as a capacitor discharges

Answer 25

P.d across capacitor decreases gradually as it loses charge, V=IR

Also, the electrostatic force between electrons that repels them to each decreases as the number of electrons decreases

Question 26

How do you show that a quantity changes exponentially

Answer 26

Show that the amount that it changes by each time changes by the same factor each time

Question 27

Define the time constant

Answer 27

Time taken to discharge a capacitor to 37% of its initial charge

This value x5 gives you the time taken to (basically completely) discharge a capacitor to 99% of its original charge

Question 28

How to calculate the time constant

Answer 28

RC

Time when the value is 0.37xthe initial Current/Voltage/Charge for a discharging capacitor

Time when the value is 0.63xthe initial Current/Voltage/Charge for a charging capacitor

Question 29

How to calculate the time taken for Charge/Voltage/Current to half

Answer 29

Time constant x ln2

Question 30

What happens to the energy stored in a charged capacitor that isn’t connected to a circuit when a dielectric is removed from it

Why?

Answer 30

Energy stored increases

In dielectric, polar molecules align in the field with positive end toward the negative plate

Work is done on the capacitor separating the positive surface of the dielectric from the negative plate

Question 31

When a question asks for something when the ratio/% of charge/I/V to the original charge/I/V … is

eg. time taken for capacitor to discharge to 1% of its original charge

What is the best thing to do

Answer 31

Rearrange equations for charging/discharging

Q/Q₀ = e^-t/RC