Capacitors

Question 1

What do capacitors do? What is its effect?

Answer 1

• Capacitors build up charge on plates
• They are components of electrical circuits that temporarily store electric charge
• They can introduce a time delay into the circuit
• Or storing electrical energy for a short period of time
• They are used extensively in electrical and electronic timing circuits, in power circuits, for smoothing electrical signals and as part of the signal receiving circuits found in radios

Question 2

How can you increase capacitance ? What is permittivity?

Answer 2

• You can increase capacitance using dielectrics
  1. Permittivity is a measure of how difficult it is to generate an electric field in a certain material
  2. The relative permittivity is the ratio of the permittivity of a material to the permittivity of free space
  3. Relative permittivity is sometimes also called the dielectric constant

Question 3

How do you work out relative permittivity?

Answer 3

Er = E1 / E0
- where Er is the relative permittivity of material 1, E1 is the permittivity of material 1 in Fm^-1, E0 is the permittivity of free space

Question 4

What happens when no charge is applied?

Answer 4

1. Imagine a dielectric is made up of lots of polar molecules - they have a positive need and a negative end
2. When no charge is stored by the capacitor, there is no electric field - so these molecules point in a bunch of random directions

Question 5

What happens when a charge is applied?

Answer 5

1. When a charge is applied to a capacitor, an electric field is generated
2. The negative ends of the molecules are attracted to the positively charged plate and vice versus
3. This causes all of the molecules to rotate and align themselves with the electric field
4. The molecules each have their own electric field, which in this alignment now opposes the applied electric field of the capacitor the larger the permittivity, the large this opposing field is
5. This reduced the overall electric field, which reduces the potential difference needed to charge the capacitor, so the capacitance increases

Question 6

How do you calculate the capacitance of a capacitor using the dimensions of the capacitor and permittivity of the dielectric?

Answer 6

C = AE0Er / d
-Where A is the area of the plates (m^2), E0 is the permittivity of free space (Fm^-1), Er is the relative permittivity of the dielectric and d is the separation of the plates (m)

Question 7

How do capacitors store energy?

Answer 7

1. When charge builds up on the plates of a capacitor, electrical energy is stored by the capacitor,
2. You can find the energy stored in the capacitor from the areas under a graph of charge stored against potential difference across the capacitor
3. The potential difference across the capacitor is directly proportional to the charge stored on it, so the graph will be a straight line though the origin
4. The greater the capacitance, the more energy is stored by the capacitor for a given potential difference

Question 8

How do you work out energy stored in a capacitor?

Answer 8

E = 1/2 Q.V.

• Where E is the energy stored (J), Q is the charge on the capacitor (C) and V is the potential difference (V)
• The gradient of a Q-V graph effectively gives the capacitance

Question 9

What are the three expressions for the energy stored by a capacitor?

Answer 9

• E = 1/2 Q.V.
• E = 1/2 CV^2
• E = 1/2 x Q^2 / C

Question 10

How can you investigate what happens when you charge a capacitor?

Answer 10

1. Set up the test circuit shown in the circuit diagram (Diagram)
2. Close the switch to connect the uncharged capacitor to the dc power supply
3. Let the capacitor charge whilst the data logger records both the potential difference (from the voltmeter) and the current (from the ammeter) over time
4. When the current through the ammeter is zero, the capacitor is fully charged

Question 11

How can you plot graphs of current, potential difference and charge against time?

Answer 11

• Diagrams
• Once a capacitor begins charging
  1. As soon as the Switch closed, current starts to flow. The electrons flow onto the plate connected to the negative terminal of the dc power supply, so a negative charge builds up
  2. This build-up of negative charge repels electrons off the plate connected to the positive terminal, making the plate positive. These electrons are attracted to the positive terminal of the power supply
  3. An equal but opposite charge builds up on each plate, causing a potential difference between the plates. Remember that no charge can flow between the plates because they are sprayed by an insulator (a vacuum, gap or dielectric)
  4. As charge builds upon the plates, electrostatic repulsion makes it harder and harder for more electrons to be deposited. When the pd across the capacitor is equal to the of across the power supply, the current falls to zero

Question 12

How do you discharge a capacitor?

Answer 12

• To discharge a capacitor remove the power supply and close the switch
  1. Remove the power supply from the test circuit and close the switch to complete the circuit
  2. Let the capacitor discharge whilst the data logger records potential difference and current over time
  3. When the current through the ammeter And the potential difference across the plates are zero, the capacitor is fully discharged

Question 13

Describe the plots of current, pd and charge against time with discharging

Answer 13

• DIAGRAMS
  1. The current flows in the opposite direction form the charging current
  2. As the potential difference decreases, the current decreases as well
  3. When a capacitor is discharging, the amount of charge on and potential difference between the plates falls exponentially with time. That means it always takes the same length of time for the charge or potential difference to halve, no matter what value it starts at - like radioactive decay
  4. The same is true for the amount of current flowing around the circuit

Question 14

What does the time taken to charge or discharge depend on?

Answer 14

• The time it takes to charge or discharge a capacitor depends on:
  1. The capacitance of the capacitor (C). This affects the amount of charge that can be transferred at a given potential difference
  2. The resistance of the circuit (R). This affects the current in the circuit

Question 15

How can you calculate the charge, pd and current as a capacitor charges?

Answer 15

1. When a capacitor is charging, the growth rate of the amount of charge on and potential difference across the plates shows exponential decay (so over time they increase more and more slowly)
2. The charge on the plates at a given time after a capacitor begins charging is given by the equation:
   - Q = Q0 (1-e^-t/RC), where Q0 is the charge of the capacitor when it is fully charged (C), t is the time since charging began (s), R is the resistance (ohms) and C is the capacitance (F)
3. The potential difference between the plates at a given time is given by V=V0 (1-e^t/RC)
4. The charging current is different however as it decreases exponentially - the formula to calculate the charging current at a given time is: I=I0e^-t/RC

Question 16

How do you work out the charge, pd and current as a capacitor discharges?

Answer 16

1. Because the amount of charge left on the plates falls exponentially with time as a capacitor discharges, it always takes the same length of time for the charge to halve, no matter how much charge you start with
2. The charge left on the plates at a given time after a capacitor begins discharging from being fully charged is given by the equation: Q=Q0e^-t/RC
3. As the potential difference and current also decrease exponentially as a capacitor discharges, the formulas for calculating current or potential difference at a certain time are similar: I-I0e^-t/RC and V=V0e^-t/RC
   - The formula for discharging current is the same as for the charging current: it just travels in the opposite direction of the charging current

Question 17

What is the time constant?

Answer 17

tau = RC

• If t=RC is put into the discharging equations above Q=Q0e^-1, V=V0e^-1, I=I0e^-1, so when t=tau, Q/Q0 = 1/e = 1/2.718 = 0.37
  1. Tau is the time constant, is the time taken for the charge, potential difference or current of a discharging capacitor to fall to 37% of its value when fully charged
  2. It is also the time taken for the charge or potential difference of a charging capacitor to rise to 63% of its value when fully charged
  3. So the larger the resistance in series with the capacitor, the longer it takes to charge or discharge
  4. In practice, the time taken for a capacitor to charge or fully discharge is taken to be about 5RC

Question 18

How can you find the time constant from log-linear graphs?

Answer 18

• Instead of using tau=RC, you can create log-linear graphs from data to find the time constant. here charge is sued, but this works for potential difference and current as well
  1. Stating from the equation for Q on a discharging capacitor, take the natural log of both sides and rearrange so that Q=Q0e^-tc becomes ln(Q) = (-1/RC)t + ln(Q0)
  2. The equation is now in the from of y=mx + c and this means that if you plotted a graph of ln(Q) against time, t, you would get a straight line
  3. The gradient of this line would be -1/RC or -1/tau and the y-intercept would be ln(Q0)
  4. To get the time constant from the graph, you divide -1 by the gradient of the the line
• For this you need to use the log rule: ln(A x B) = ln(A) + ln(B) and ln(e^A) = A

Question 19

How do you figure out the time taken for chagre current or pd to halve?

Answer 19

• Time to halve, T1/2 = 0.69RC
  1. The ‘time to halve’ is the time taken for the charge, current or potential difference of a discharging capacitor to reach ha;f of the value it was when it was fully charged
• T1/2 = 0.69RC (where T1/2 is the time to halve (s), R is the resistance in the circuit (ohms) and C is the capacitance of the capacitor (F)
• Example!

Question 20

What are capacitors made of?

Answer 20

1. A capacitor is an electrical component made up of two parallel conducting plates (usually made of metal foils, films or coatings) separated by a thin insulating layer known as a dielectric (an insulating material, generally made from thin plasticise electrolytes ceramics or metal oxides)
2. When a capacitor is connected to a power source, positive and evasive charge build up on opposite plates, creating a uniform electric field between them

Question 21

What happens to a capacitor when it is connected to a power source?

Answer 21

1. A potential difference from a battery or a power supply is commuted across the metal plates causes electrons to flow off one plate, back through the battery and onto the second plate
2. Positive (where electrons are removed) and negative (excess of electrons) charge build up on opposite plates, creating a uniform electric field between them
3. The amount charge per unit potential difference (voltage) stored by a capacitor is called its capacitance
   - C = Q/V where Q is the charge in coloumbs, V is the potential difference in volts and C is the capacitance in farads (F) - 1 farad = 1CV^-1
4. A farad is a huge unit so you’ll usually see capacitances expressed in terms of smaller units so remember to convert

Question 22

What happens to the capacitor when the capacitor is disconnected from the source of potential difference?

Answer 22

• The charge will stay on the plates until a conducting pathway allows the excess electrons to flow off the negatively charged plate and back onto the positive plate, until the two plates have an equal charge again
• The conducting pathway could be a different part of the circuit (controlled by a switch) or the charge could gradually leak away to the surroundings

Question 23

What is the capacitance of a capacitor? What does it depend on?

Answer 23

• It is the ability of the capacitor to store charge per unit potential difference
• The capacitance of a capacitor depends on:
  1. The area of the metal plates
  2. The distance between the plates
  3. The electrical poetries of the material separating the plates (ability of the insulting material between the plates to separate the change (permittivity))

Question 24

What is a farad?

Answer 24

The unit of capacitance is the farad (F) where 1F is equal to 1C^-1 (one colomb per volt)

Question 25

What is the equation for the capacitance of a capacitor?

Answer 25

• The amount of charge, Q, that can be stored on a capacitor depends on the size of the capacitance, C and the potential difference V, across the capacitor causing the separation of the charge
• C=Q/V
• A capacitance of 1F will store a charge of 1C with a potential difference of 1V across it

Question 26

What is permittivity?

Answer 26

The permittivity of a material is the resistance of the material to an electric field passing through it

Question 27

What is the dielectric constant?

Answer 27

• Another term for the relative permittivity of an insulating material
• It describe the relative resistance of the material to the propagation of electric field through it and describes the absolute permittivity of the material in terms of multiples of the permittivity of free space ErE0

Question 28

What does the capacitance of a parallel plate capacitor depend on?

Answer 28

1. The area of the plates
2. The distance between the plates
3. The ability of the insulating material between the plates to separate the charge, a property known as permittivity
   - The permittivity of a capacitor insulating materials is always measured relative to the permittivity of free space (a vacuum) E0, using a relative permittivity (Er) (The dielectric constant of the material)

Question 29

What happen if the permittivity is high?

Answer 29

Then a larger charge can be stored on the plates for any given pd across them

Question 30

How is the total absolute permittivity of an insulator given?

Answer 30

• Er x E0

- E0 is 8.854 x 10^-12

Question 31

What is the capacitance of a parallel plate capacitor?

Answer 31

C = ErE0A / d

• A is the area of the plates
• d is their separation
• The charge density on each plate is proportional to V/d which is the electric field E

Question 32

What is dielectric heating?

Answer 32

1. In polar molecules, such as water, opposite ends of the molecule have opposite charges
2. In a polar molecule, the overall charge of the molecule is zero, but different ‘end’ of the molecule may have opposite charges
3. Polar molecules easily stick to metal surface, where one end of the polar molecule induces an opposite charge in the metal, causing the molecule to be attracted to the metal surface

Question 33

What is a dielectric material?

Answer 33

An insulating material when the molecules that make up the material can be polarised inside an electric field. Electric charges do not move through the material but the polar molecules align themselves with the field

Question 34

What happens when the dielectric material is a liquid or gas?

Answer 34

1. Most of the dielectric material used to construct capacitors are solids and the atoms and molecules are sized within the structure
2. When the solid is replaced by a liquid, such as water or a gas, the electric field between the two plates of a capacitor will cause the charged particles in a liquid or gas to align themselves in the direction of the field
   - The separated charge in a polar molecules is particularly able to align itself with the field between two capacitor plates

Question 35

What happens when the electric field is suddenly reversed in a capacitor?

Answer 35

1. The polar molecule will rotate and align itself with the direction of the electric field agin
2. Alternating the electric field between the two plates will cause a polar molecule, such as water, to continuously rotate between them (called dipole rotation)
3. This increases its kinetic energy and causes it to collide with other adjacent molecules and atoms
4. These then aware more kinetic energy and move in random directions, increasing their temperature and so disputing the energy as heat

Question 36

How can the alternating field between the plates be produced?

Answer 36

By a microwave emitter, such as the magnetron inside a microwave oven. The frequency of the microwaves is turned so that it rotates water molecules within food, causing the food to heat up rapidly

Question 37

What happens as a capacitor is charging?

Answer 37

1. When a capacitor is charged up, the pd from the electricity supply (or energy per unit charge) causes electrons to flow off one plate through the external circuit and onto the other plate
2. This operation of charge is kept steady provided that the pd is continuously supplied and there is no leakage of charge
3. Once the pd is removed, and a complete discharging circuit is connected to the capacitor, the electrical energy stored by the separated charge can be released as the electrons flow back off the negatively charged plate and onto the positively charged plate
   - If the pd applied to the plates is increase, more charge and therefore energy is stored on the plates

Question 38

How does energy relate to capacitors?

Answer 38

• V=W/Q, work done per unit charge
• in the context of capacitors the V is the amount of work done in a moving init charge off one plate and onto another plate
• At any potential difference V the work done moving an amount of charge deltaQ is therefore W=VDeltaQ
• The total energy stored on the capacitor charging are capacitor from empty up to a charge of Q at a potential difference V is calculated by the area under the graph

Question 39

What happens to the current if the capacitor is initially uncharged and the circuit is switched on?

Answer 39

• The amount of charge that can be stored on it per second is deltaQ/deltat = I, is initially determined by I=V/R
• As the capacitor stays to store charges, so and is developed across the capacitor Vc = Q/C
• As the emf of the battery remains constant the potential difference across the fixed resistor R reduced because E - Vr + Vc
• Reducing Vr reduced the current I flowing
• The initial current flowing onto the capacitor gradually decays away as the capacitor stores more charge, increasing Vc
• (LOOK AT NOTES)

Question 40

What is the shape of a discharging graph and why?

Answer 40

1. The shape of the discharging graph is an exponential decay, meaning that the rate of decay of charge (or the gradient or the current) depends on the amount of change stored at any given time
2. For a discharging capacitor the current is directly proportional to the amount of charge stored on the capacitor at time t

Question 41

Why is the size of the current always at a maximum immediately after the switch is closed in the discharging or charging circuit?

Answer 41

Because the charging current will be highest when the capacitor is fully charged

Question 42

What is the time constant of a capacitor?

Answer 42

1. The quantity RC is called the time constant of a capacitor circuit
2. The time constant is related to the half life of the decay of charge of the capacitor, and is analogous to the half life of radioactive decay
3. We define the half life of capacitor discharge as the time taken for the change store on the capacitor (or the current or the voltage) to halve

Question 43

What is the equation for a straight line capacitor for exponential decay?

Answer 43

LnI = LnI0 - 1/RC t

Question 44

Describe charging a capacitor

Answer 44

1. In many cases the charging of a capacitor is designed to be as quick as possible, and so the resistance of the charging part of a capacitor circuit is kept as low as possible
2. However if the charging process is part of a circuit that requires a higher resistance the charging time must be taken into account

Question 45

What are the equations for charging a capacitor?

Answer 45

V=V0 (1-e^t/RC)
Q = Q0 (1-e^-t/RC)
I=I0e^-t/RC

Question 46

Why are dielectric material used in capacitors?

Answer 46

• Polar molecules in the material rotate under the influence of the electric field
• this attracts more charge to build up on the capacitor plates and hence increases the capacitance