Capacitors

Question 1

What is a capacitor

Answer 1

Type of electrical component made up of 2 conducting plates which is used to store charge quickly and then discharge quickly

Question 2

How does a capacitor store charge and cause a uniform electric field

Answer 2

Connect one plate to positive end of power supply and one plate to negative which causes negatively charged electrons to store up on one plate, causing a pd and uniform electric field

Question 3

Define capacitance

Answer 3

The amount of charge that a capacitor can store per volt applied between the plates

i.e. C = Q/V

Question 4

Define permittivity

Answer 4

A measure of how difficult it is to produce an electrical field in that material

Question 5

Why would a dielectric be placed in the between the plates of a capacitor

Answer 5

• Dielectric is a non-conducting material
• Increase the permittivity between plates
• Decrease electric field so less pd required to maintain the same charge
• Increased capacitance

Question 6

How does the dielectric reduce the pd between the plates

Answer 6

• Dielectric made up of polar molecules which are positive on one end and negative on other
• They orient themselves so -ve side is attracted to +ve plate and +ve side is attracted to negative plate
• This reduces the net electric field and pd between the plates

Question 7

What is relative permittivity

Answer 7

εr = permittivity of the dielectric / ε0

where ε0 is the permittivity of free space i.e. if there was no dielectric

Question 8

What is the formula relating capacitance with area of the plates, distance between the plates and permittivity of the dielectric

Answer 8

• As area increases more charged stored so C ∝ A
• As d increases E weakens so more pd required to maintain charge so C ∝ 1/d
• As permittivity of dielectric increases C increases

C = Aε0εr / d

Question 9

How can you calculate the energy stored by a capacitor

Answer 9

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

Question 10

How can you work out energy stored by a capacitor with a graph of Q against V

Answer 10

Area under the graph

Question 11

Describe the graphs of how Q, V and I change over time for a charging capacitor

Answer 11

• Q and V increases but more slowly as time increases until it plateaus at max Q or V
• I decreases from max I but more slowly as time increases until it reaches 0

Question 12

Describe the graphs of how Q, V and I change over time for a discharging capacitor

Answer 12

• Q, V and I all decrease with time but more slowly as time increases

Question 13

What is the time constant

Answer 13

Time taken for the charge, pd or current to fall to 37% of max value or rise to 63% of max value

Question 14

What is the formula for time constant

Answer 14

T = RC
so time taken to charge and discharge is determined by capacitance of capacitor and resistance of circuit

Question 15

What are the formulas for calculating charge, voltage and current at a given time

Answer 15

If the graph is decreasing:
Q = Q0 e^-t/RC
(Could be I or V as well)

If the graph is increasing:
Q = Q0 (1 - e^-t/RC)
(Could be V)

Question 16

How can you find the time constant from a graph of ln Q or ln V against t

Answer 16

gradient = -1/RC

Question 17

How can you work out the time taken for Q, V or I to half

Answer 17

0.69 RC

(Can derive this by subbing in 1/2 Q0 for Q)