Capacitors

Question 1

What are capacitors?

Answer 1

• Capacitors are electrical devices used to store energy in electronic circuits, commonly for a backup release of energy if the power fails

Question 2

What is the most common type of capacitor?

Answer 2

• The parallel plate capacitor
• Consists of two conductive plates parallel to eachother connected to a voltage supply
• They commonly have a dielectric between them

Question 3

What is a dielectric?

Answer 3

• A dielectric is a substance which is a poor conductor of electricity but a good supporter of electric fields

Question 4

Why is there a dielectric in capacitors?

Answer 4

• To ensure charge does not flow freely between the plates

Question 5

What is capacitance?

Answer 5

• The charge stored per unit potential difference between the plates
• The higher the capacitance, the greater the amount of energy stored in the capacitor
• C = Q / V

Question 6

What is Q in the capacitance equation?

Answer 6

• Q is the charge stored ON the plates, not the charge of the capacitor itself

Question 7

What is a dielectric made up of?

Answer 7

• A dielectric is made up of many polar molecules that have positive and negative ends

Question 8

What happens to the dielectric when no charge is applied to a capacitor?

Answer 8

• There is no electric field between the plates and the molecules are aligned in random directions

Question 9

What happens to the dielectric when charge is applied to a capacitor?

Answer 9

• One of the parallel plates becomes negatively charged and the other becomes positively charged
• This causes an electric field between the plates (positive to negative)
• The negative ends of the polar molecules are attracted to the positive plate and vice versa
• This means all of the molecules rotate and align themselves parallel to the electric field

Question 10

What is permittivity?

Answer 10

• The measure of how easy it is to generate an electric field in a certain material

Question 11

What is the relative permittivity?

Answer 11

• The relative permittivity is also known as the dielectric constant
• It is defined as the ratio of the permittivity of a material to the permittivity of free space
• It has no units as it is a ratio
• εr = ε / ε0

Question 12

What happens when the polar molecules in a dielectric align?

Answer 12

• The polar molecules all produce their own electric field
• This opposes the electric field from the plates
• The larger the opposing electric field from the polar molecules in the dielectric, the larger the permittivity

Question 13

What is the connection between the permittivity and the polar molecules?

Answer 13

• The permittivity can be referred to as how well the polar molecules in a dielectric align with an applied electric field

Question 14

How does a dielectric increase the capacitance?

Answer 14

• The opposing electric field from the polar molecules reduces the overall electric field, which decreases the potential difference
• As C = Q / V, a lower potential difference leads to a greater capacitance

Question 15

How can you calculate the capacitance of a capacitor in terms of permittivity?

Answer 15

• C = Aε0εr / d
• A = cross-sectional area of the plates
• d = separation of the plates
• ε0 = permittivity of free space
• εr = relative permittivity

Question 16

What happens to the electrons when you charge a capacitor?

Answer 16

• The power supply pushes electrons onto the negative plate and pulls electrons from the positive plate
• The power supply, therefore, does work on the electrons, and electrical energy becomes stored on the plate

Question 17

What path do electrons follow when a capacitor charges?

Answer 17

• Electrons flow from the negative terminal of the power supply to the negative plate of the capacitor
• From the positive plate of the capacitor to the positive terminal of the power supply

Question 18

Why does it become harder to push electrons on a capacitor?

Answer 18

• At first, a small amount of charge is pushed from the negative plate to the positive plate, then gradually, this builds up
• Adding more electrons to the negative plate at first is relatively easy as there is little repulsion

Question 19

What happens as more charge becomes stored on a capacitor?

Answer 19

• As the charge on the negative plate increases (becomes more negatively charged), the force of repulsion between the electrons on the plate and the new electrons being pushed onto it increases
• This means a greater amount of work must be done to increase the charge on the negative plate

Question 20

How is the potential difference across a capacitor and the charge stored on the capacitor related?

Answer 20

• As the potential difference across the capacitor increases, the amount of charge increases
• The charge Q on the capacitor is directly proportional to its potential difference V

Question 21

What are the characteristics of a potential-charge graph?

Answer 21

• The graph of charge against potential difference is a straight line through the origin
• The area under the graph is equal to the electrical potential energy stored in the capacitor

Question 22

When does a capacitor stop charging?

Answer 22

• As the negative charge on builds up, fewer electrons are pushed onto the negative plate due to electrostatic repulsion from the electrons already on the plate
• When no more electrons can be pushed onto the plate, the charging stops

Question 23

How does the current change over time when charging a capacitor?

Answer 23

• At the start of charging, the current is large and gradually falls to zero as the electrons stop flowing through the circuit
• The current decreases exponentially
• The rate at which the current decreases is proprtional to the amount of current left: if the current is large, it decreases quickly vice versa

Question 24

How does the potential difference change when charging a capacitor?

Answer 24

• Since an equal but opposite charge builds up on each plate, the potential difference between the plates slowly increases until it is the same as that of the power supply

Question 25

How does the charge change as the capacitor is charged

Answer 25

- The charge of the plates slowly increases until it's at its maximum charge defined by the capacitance of the capacitor

Question 26

What are the graphs for chagring a capacitor?

Answer 26

- Current-time: exponential decay - Voltage-time: increases with a decreasing gradient - Charge-time: increases with a decreasing gradient

Question 27

How are capacitors discharged?

Answer 27

- Capacitors are discharged through a resistor with no power supply present - The electrons now flow back from the negative plate to the positive plate until there are an equal number of electrons on each plate and no potential difference between the plates

Question 28

How is a circuit set up to allow you to charge or discharge a capacitor?

Answer 28

- Commonly achieved by moving a switch which connects the capacitor between a power supply and a resistor

Question 29

How does the current change as a capacitor discharges?

Answer 29

- At the start of discharge, the current is large (moving in the opposite direction to when it was charging) and gradually falls to zero

Question 30

What are the graphs for discharging a capacitor?

Answer 30

- Current-time: exponential decay - voltage-time: exponential decay - Charge-time: exponential decay

Question 31

How does the resistance of the resistor effect the discharge of a capacitor?

Answer 31

- If the resistance is high, the cuerrent will decrease and charge will flow slower, meaning the capacitor will take longer to discharge - If the resistance is low, the current will increase and charge will flow faster, meaning the capacitor will take less time to discharge

Question 32

What is the area under a current-time graph?

Answer 32

- The area under a current-time graph is equal to the charge stored for a certain time interval by a capacitor

Question 33

What is the gradient of a current-time graph?

Answer 33

- The gradient of a current-time graph is the current in the circuit at that time - In the discharging graph, this is the discharing current at that time - In the charging graph, this is the charging current at that time

Question 34

What is the time constant for a discharging capacitor?

Answer 34

- The time taken for the charge, voltage or current of a discharging capacitor to decrease to 37% of its original value

Question 35

What is the time constant for a charging capacitor?

Answer 35

- The time taken for the charge or voltage of a charging capacitor to reach 63% of its maximum value

Question 36

What is time constant measured in and what's it useful for?

Answer 36

- Time constant is represented with 𝜏 and is measured in seconds - It is a useful way of comparing the rate of change of similar quantities

Question 37

How do you calculate the time constant?

Answer 37

- 𝜏 = RC - 𝜏 = time constant (s) - R = resistance of the resistor (Ω) - C = capacitance of the capacitor (F)

Question 38

What does the exponential decay when discharging a capacitor tell us about the charge?

Answer 38

- No matter the amount of charge left on the capacitor plate, the time taken for the charge to halve is the same

Question 39

What is the discharging capacitor equation for current?

Answer 39

- I = I0e^(-t/RC) - I0 = initial current before discharge - t = time - RC = time constant

Question 40

What is the discharging capacitor equation for charge?

Answer 40

- Q = Q0e^(-t/RC) - Q0 = initial charge before discharge - t = time - RC = time constant

Question 41

What is the discharging capacitor equation for current?

Answer 41

- V = V0e^(-t/RC) - V0 = initial potential difference before discharge - t = time - RC = time constant

Question 42

What does the discharge equation tell us about the current through a capacitor?

Answer 42

- The smaller the time constant, the quicker the exponential decay of the current when discharging - The greater the initial current, the longer it will take for the capacitor to discharge

Question 43

What is the true definition of the time constant (in terms of e)

Answer 43

- The time constant is the time taken for the charge of a capacitor to decrease to 1/e of its original value - 1/e ≈ 0.37

Question 44

How do the values change when charging a capacitor?

Answer 44

- The charge Q and potential difference V increase exponentially. Over time, they continue to increase at a slower rate - The current decreases exponentially

Question 45

What is the charging capacitor equation for charge?

Answer 45

- Q = Q0 (1 - e^-t/RC) - Q0 = maximum charge stored on plates when fully charged

Question 46

What is the charging capacitor equation for potential difference?

Answer 46

- V = V0 (1 - e^-t/RC) - V0 = maximum potential difference stored on plates when fully charged

Question 47

What is the charging capacitor equation for current?

Answer 47

- The charging equation for the current is the same as its discharging equation as they both decrease exponentially - I = I0e^(-t/RC)