Capacitance

Question 1

What is relative permittivity (Dielectric constant) ?

Answer 1

The ratio of charged stored with the dielectric between the plates and the charge stored with the direlectric not present

The greater the relative permittivity the greater the capacitance of the capacitor

Question 2

What does the area beneath a charge against Potential difference graph represent?

Answer 2

The electric potential energy stored by the capacitor

Question 3

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

Answer 3

As the capacitor discharges the charge it currently stores decreases

The rate that the charge decreases, slows down over time.

Charge = 0 acts as an asymptote and the total charge cannot go below this value.

Question 4

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

Answer 4

As the capacitor discharges the potential difference across the plates decreases

The rate that potential difference decreases between the plates, slows down over time.

Potential difference = 0 acts as an asymptote and the potential difference cannot go below this value.

Question 5

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

Answer 5

As the capacitor discharges the current induced by the potential difference decreases

The rate that the current decreases, slows down over time.

Current = 0 acts as an asymptote and the Current cannot go below this value.

Question 6

Describe a Q against T Graph for the charging of a capacitor through a resistor

Answer 6

As the capacitor charges, the charge it currently stores increases

The rate that the charge increases, slows down over time.

The value when charge = capacitance*terminal pd acts as an asymptote and the charge cannot go above this value.

Question 7

Describe a V against T Graph for the charging of a capacitor through a resistor

Answer 7

As the capacitor charges the potential difference across the plates increases

The rate that potential difference increases between the plates, slows down over time.

The terminal Potential difference of the cell charging it acts as an asymptote and the potential difference cannot go above this value.

Question 8

What is the Time constant

Answer 8

The time it take for the change in the capacitor to fall to 1/e or 37% of the initial value

Question 9

After how many time constants is a capacitor considered ‘Fully Discharged’

Answer 9

5

Question 10

What is the equation for the amount of the potential difference between the plates, when a capacitor is discharging

What is the equation for the amount of the current, when a capacitor is discharging

Answer 10

V = (Initial V)*e^(-t/RC)

As current and voltage are directly proportional
therefore

I = (Initial I)*e^(-t/rC)

Question 11

What is the equation for the amount of the potential difference between the plates, when a capacitor is Charging

Answer 11

V = (Initial V)* ( 1 - e^(-t/RC) )

Question 12

How does a capacitor Charge up? (6)

Answer 12

Electrons flow from negative plate in the battery to the positive plate (opposite to current)

Electrons accumulate on one of the sides of the capacitor, this causes negative charge to build on that plate

The negatively charged plate repels electrons original present in the metal of the adjacent plate around the circuit

This creates a flow of charge

Meaning the adjacent plate becomes positively charged

The oppositely charged plates store electric potential energy which increases over time as the potential difference between the plates increase until a certain point

Question 13

State 3 expressions for the energy stored by a capacitor

Answer 13

E = 1/2 * (Q^2 / C )

E = 1/2 * QV

E = 1/2 * CV^2

Question 14

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

Answer 14

Capacitance - Amount of charge that can be stored at any given potential difference across it

Resistance of Circuit -How quickly the charge is dissipated from the capacitor

Question 15

What is Capacitance

Answer 15

The amount of charged stored per unit volt in a device or capacitor

Question 16

Explain why a larger plate will store more charge, have a larger capacitance

Answer 16

The charge is distributed over a larger area

It is possible to store more electrons on the negative plate

Less potential difference for the same number of electrons on the larger negative plate, more charge can be stored per unit volt

Question 17

What are Dielectrics?

How do they improve the performance of a capacitor?

Answer 17

• Electrically insulating materials placed between the plates of a. capacitor

2)

• they prevent the plates from touching each other on the capacitor
• they increase the capacitance of the material

Question 18

How do dielectrics increase the capacitance of a capacitor (5)

Answer 18

Molecules within the dielectric material are polarised

Polar molecules align with their positive dipole facing the negative plate

producing a counter electric field between the plates

as a result potential difference reduced between the capacitor plates but the charge remains the same

so more charge can be stored per unit volt, capacitance has increased

Question 19

How does a capacitor store electrical potential energy

Answer 19

although capacitor remains neutral and no net charge is stored

the difference in opposite charge creates an electric field

Question 20

How do you calculate the time taken for a capacitor to charge to a certain charge

Answer 20

1) use Q = (initial Q) * (1-e^(-t/RC)

2) sub (initial Q) in for Capacitance * Peak Voltage

Question 21

Dielectric Constant = 6

Charge stored without dielectric = 7.2x10^-10 coulombs

Capacitance without dielectric = 63 picofarads

What is the difference in energy stored between the capacitor with dielectric and without a dielectric

Answer 21

Q remains the same
However capacitance with dielectric is 6x then without

E =1/2* Q^2 / C

Energy difference = -3.4x10^-9 (but take positive magnitude)

Question 22

Answer 22

constant angular velocity
constant decrease in area between plates
constant decrease in capacitance

Question 23

What is the Half time of a Capacitor

Answer 23

Time Constant * ln(2)

Question 24

Answer 24

B

Question 25

Answer 25

C

Question 26

Answer 26

Question 27

State two factors of a capacitors design that affect its performance

Answer 27

Area of overlap between capacitor plates

Distance between the Capacitor plates.

Question 28

A uncharged capacitor is charged by a constant current of 4.5 Micro Amps for 60 seconds, The PD across it becomes 4.4 volts.

A battery that produces 6 volts of terminal voltage charges the capacitor.
In order to keep the current constant the variable resistor in the circuit decreases steadily as the charge of the capacitor increases.

Calculate the resistance of R when the uncharged capacitor has been charging for 30 seconds.

Answer 28

At T=30 Voltage is equal to 2.2v as a constant current charges the capacitor which is proportional to voltage. 30/60 = X/4.4

R = V/I

R= 8.4X10^5

Question 29

Describe how the potential differences across the resistor and capacitor change over time while the circuit is charging and discharging

Answer 29

Charging:
V(resistor) decreases from the cells terminal voltage to zero
V(capacitor) Increases from zero to Cells terminal voltage
At any time Vr+Vc = Cells terminal voltage
V(resistor) is exponential decrease
V(capacitor) is exponential increase

Discharging:
V(capacitor) decreases from -1*cells terminal voltage to zero (current moves in opposite direction to charging)
V(resistor) decreased from cells terminal voltage to zero
At any time V(capacitor) = —V(resistor)
Both V(resistor) and V(capacitor) decrease exponentially with time

Question 30

Describe the energy changes that take place in the circuit in charging and discharging

Answer 30

Charging:
Chemical Energy form battery is converted to electrical potential energy within the capacitor
and thermal energy by the resistor, which is dissipated into surroundings

Discharging:
Electrical potential energy in the capacitor is all converted to thermal energy by the resistor

Question 31

State and explain whether capacitors B has a Larger or Smaller Capacitance then A

Answer 31

B discharges faster then A

V=V(o)*e^-t/RC

For all values of t in e^-t/RC , B is smaller then A. So time constant in capacitor B is greater then time constant in capacitor A .

Same values of Resistance

Question 32

Explain what is meant by a dielectric constant of 6

Answer 32

The permitting it’s of the dielectric is 6 times the permittivity of free space