Section 10 - Capacitors Flashcards
What is a capacitor?
- An electrical component made up of two conducting plates separated by a gap or a dielectric.
- Used to store opposing charges and therefore energy.
What is a dielectric?
An insulating material placed between the two plates of a capacitor.
What is the name of the most common type of capacitor?p
Parallel plate capacitor
What happens when a capacitor is connected to a power source (d.c.)?
• Positive and negative charges build up on opposite plates
• Uniform electric field is created between the plates
Potential difference builds up between the plates?
Why does potential difference build up between the plates on a capacitor?
Plates are separated by an electrical insulator, so no charge can move between them.
What is capacitance?
The charge stored per unit potential difference by a capacitor. quote formula
What is the symbol for capacitance?
C
What is the unit for capacitance?
Farad (F)
C = Q / V is found on the data sheet
what do the symbols stand for?
C = Q / V
Where:
• C = Capacitance (F)
• Q = Charge (C)
• V = Potential difference (V)
How many farads is a μF?
10^-6
How many farads is a nF?
10^-9
How many farads is a pF?
10^-12
What units are capacitance values usually in and why?
- From microfarads to picofarads
* Because a farad is a huge unit
What is the voltage rating of a capacitor?
The maximum potential difference that can be safely put across it.
How can a bucket represent a capacitor?
What is the relationship of Q and V?
Q is directly proportional to V.
How can use investigate the relationship with Q and V with a capacitor and variable resistor?
When investigating the relationship with Q and V, what does the graph of current against time look like?
How can you find the charge?
What does the graph of Q-V look like?
What is the gradient?
Straight line through origin.
Gradient is capacitance
How long do capacitors provide power for?
short amount of time
As capacitor discharges, what decreases?
Voltage through the circuit
Why are capacitors dangerous?
They can store charge until needed and then discharge all of their charge in a fraction of a second.
The capacitors contain enough charge to kill you
What are some examples of capacitors?
Camera flash.
Back-up power supplies - using ultracapacitors - reliable power for short periods of time.
Smoothing out variations in D.C. voltage supplies - capacitor absorbs the peaks and fills in the troughs.
What is permittivity?
A measure of how difficult it is to generate an electric field in a certain material.
What is relative permittivity?
The ratio of permittivity of a material to the permittivity of free space.
If permittivity is high, does it require more or less charge to generate an electric charge?
More charge
What is the symbol for relative permittivity?
εr (where r is subscript)
What is the unit for permittivity?
F/m
What is the equation that defines relative permittivity?
εr = ε₁ / ε₀
Where:
• εr = Relative permittivity
• ε₁ = Permittivity of material 1 (F/m)
• ε₀ = Permittivity of free space (F/m)
(NOTE: Not given in exam)
What are the units for relative permittivity?
No units
ratio
What is another name for relative permittivity?
Dielectric constant
Describe how a dielectric works.
When no charge is applied:
• Dielectric is made up of lots of polar molecules
• These all point in random directions
When charge is applied:
• Electric field is generated
• Negative ends of molecules are attracted to positive plate and vice versa, causing them to rotate and align with the electric field
• The molecules each have their own electric field which opposes the applied field of the capacitor. The larger the permittivity, the larger the opposing field is.
• The reduces the overall electric field, which reduces the potential difference needed to charge the capacitor.
• This means the capacitance increases.
Describe how a dielectric behaves when no charge is applied to the capacitor.
- Dielectric is made up of lots of polar molecules
* These all point in random directions
Describe how a dielectric behaves when a charge is applied to the capacitor.
- Electric field is generated
- Negative ends of molecules are attracted to positive plate and vice versa, causing them to rotate and align with the electric field
- The molecules each have their own electric field which opposes the applied field of the capacitor. The larger the permittivity, the larger the opposing field is.
- The reduces the overall electric field, which reduces the potential difference needed to charge the capacitor.
- This means the capacitance increases
How does a larger permittivity of the dielectric affect the capacitance and why?
- The larger the permittivity, the larger the capacitance.
- Because a larger permittivity means the opposing field produced by the dielectric molecules is larger, so the potential difference needed to charge the capacitor decreases, which increases the capacitance.
Give the equation for the capacitance of a capacitor relative to its dimensions and permittivity of the dielectric.
C = Aε₀εr / d
Where: • C = Capacitance (F) • A = Area of the plates (m²) • ε₀ = Permittivity of free space (F/m) • εr = Relative permittivity of the dielectric • d = Separation of the plates (m)
How can you investigate how capacitance changes (C = Aε₀εr / d)?
What else do capacitors store except for charge?
Energy
Why is energy required when capacitors charge?
When a plate of a capacitor becomes charged, the charges on the plate are being forces together “against their will” (like charges repel).
Describe the Q-V graph for a capacitor.
Straight line of positive gradient through the origin.
How can energy stored in a capacitor be found from the Q-V graph?
It is the area under the graph.
How is capacitance related to energy stored by the capacitor?
The greater the capacitance, the more energy is stored by the capacitor for a given potential difference.
If energy supplied in charging a capacitor is E = VQ and energy stored in the capacitor is E = 1/2 VQ, then were is the other half of the energy stored?
Energy stored by the capacitor is half the energy supplied to the capacitor.
The rest is lost to the resistance of the circuit and the internal resistance of the battery.
Give the 3 equations for the energy stored by a capacitor.
E = 1/2 x Q x V OR E = 1/2 x C x V² OR E = 1/2 x Q² / C
Describe the circuit used to investigate capacitor charging and discharging.
- Capacitor is in series with resistor, ammeter and power supply
- Voltmeter around capacitor
- Ammeter and voltmeter connected to data logger
(See diagram pg 134 of revision guide)
Describe how charging a capacitor can be investigated.
- Set up equipment as shown
- Close the switch to connect the uncharged capacitor to the power supply
- Let the capacitor charge while the data logged records the potential difference and current
- When the ammeter reading is 0, the capacitor is fully charged
Describe what occurs when a capacitor starts charging (in terms of charge, current and and pd).
1) When switch is closed, current starts to flow.
2) Electrons flow onto the plate connected to the negative terminal, which causes negative charge to build up.
3) This charge repels electrons off the other plate, causing it to become positive. The electrons are attracted to the positive terminal.
4) Equal but opposite charge on each plate causes a potential difference to be created.
5) As charge builds up on the plates, it becomes harder to more electrons to be deposited due to electrostatic repulsion.
6) When the pd is equal to the power supply pd, the current falls to 0.
What stops current flowing between the two plates on a capacitor?
The insulator between then.
What causes the potential difference across a capacitor?
The opposite charges on each plate.
What happens to current as a capacitor charges?
It slows down until it reaches zero due to the increased electrostatic repulsion making it harder for electrons to be deposited.
When does the current fall to zero in charging a capacitor?
When the potential difference across the capacitor equals the potential difference across the power supply.
Describe the I-t graph for a capacitor charging.
- Starts at positive y-intercept
- Current decreases at decreasing rate
- Eventually reaches 0
Describe the V-t graph for a capacitor charging.
- Starts at origin
- P.d. increases at decreasing rate
- Eventually reaches peak p.d.
Describe the Q-t graph for a capacitor charging.
- Starts at origin
- Charge increases at decreasing rate
- Eventually reaches peak charge
How can charge be found from an I-t graph for a capacitor charging?
- It is the area under the curve
* Because Q = I x t
Describe how discharging a capacitor can be investigated.
- Set up equipment as shown
- First, charge the capacitor fully
- Close the switch to complete the circuit
- Let the capacitor charge while the data logged records the potential difference and current
- When the ammeter reading is 0, the capacitor is fully discharged
Describe the I-t graph for a capacitor discharging.
- Starts at positive y-intercept
- Current decreases at decreasing rate
- Eventually reaches 0
Describe the Q-t graph for a capacitor discharging.
- Starts at positive y-intercept
- Current decreases at decreasing rate
- Eventually reaches 0
Describe the V-t graph for a capacitor discharging.
- Starts at positive y-intercept
- Current decreases at decreasing rate
- Eventually reaches 0
What is Q₀ in capacitors?
The charge across a capacitor when it’s fully charged.
What is V₀ in capacitors?
The potential difference across a capacitor when it’s fully charged.
What is I₀?
The current in a capacitor circuit when charging or discharging it is started.
What are Q₀, V₀ and I₀?
The peak values for each of charge, potential difference and current in a capacitor.
Does current flow in the same direction when charging and discharging a capacitor?
No, in opposite directions.
Remember to practice drawing out the I-t, Q-t and V-t graphs for capacitor charging and discharging.
Pages 134 and 135 of revision guide or page 314 and 315 of the textbook.
What does the time taken to charge or discharge a capacitor depend on?
- Capacitance (C)
* Resistance (R)
Why does capacitance affect the time to charge or discharge a capacitor?
Capacitance affects the amount of charge that can be transferred at a one potential difference.
(Since C = Q/V)
Why does the resistance of the circuit affect the time to charge or discharge a capacitor?
The resistance affects the current in the circuit.
Describe how charge, potential difference and current change with time as a capacitor is charged.
CHARGE AND POTENTIAL DIFFERENCE:
• Increase with exponential decay
• So over time they increase more and more slowly
CURRENT:
• Decreases with exponential decay
• So over time they decrease more and more slowly
Give the equation for the charge across a capacitor as it is charged.
Q = Q₀(1 - e^(-t/RC) )
Where: • Q = Charge of capacitor (C) • Q₀ = Charge of capacitor when fully charged (C) • t = Time since charging began (s) • R = Resistance (Ω) • C = Capacitance (F)
Give the equation for the potential difference across a capacitor as it is charged.
V = V₀(1 - e^(-t/RC) )
Where: • V = P.d. across capacitor (V) • V₀ = P.d. across capacitor when fully charged (V) • t = Time since charging began (s) • R = Resistance (Ω) • C = Capacitance (F)
Give the equation for the current in capacitor circuit as it is charged.
I = I₀e^(-t/RC)
Where: • I = Current (A) • I₀ = Current when charging is started (A) • t = Time since charging began (s) • R = Resistance (Ω) • C = Capacitance (F)
Describe how charge, potential difference and current change with time as a capacitor is discharged.
CHARGE AND POTENTIAL DIFFERENCE:
• Increase with decrease decay
• So over time they decrease more and more slowly
CURRENT:
• Increases with exponential decay
• So over time they increase more and more slowly
Give the equation for the charge across a capacitor as it is discharged.
Q = Q₀e^(-t/RC)
Where: • Q = Charge of capacitor (C) • Q₀ = Charge of capacitor when fully charged (C) • t = Time since charging began (s) • R = Resistance (Ω) • C = Capacitance (F)
Give the equation for the potential difference across a capacitor as it is charged.
V = V₀e^(-t/RC)
Where: • V = P.d. across capacitor (V) • V₀ = P.d. across capacitor when fully charged (V) • t = Time since charging began (s) • R = Resistance (Ω) • C = Capacitance (F)
Give the equation for the current in capacitor circuit as it is discharged.
I = I₀e^(-t/RC)
Where: • I = Current (A) • I₀ = Current when discharging is started (A) • t = Time since charging began (s) • R = Resistance (Ω) • C = Capacitance (F)
What is the symbol for the time constant?
τ
What is the time constant, τ, when discharging?
- The time taken for the charge, potential difference or current of a capacitor to fall to 37% of its value when fully charged.
- It is equal to RC.
What is the time constant, τ, when charging?
- The time taken for the charge or potential difference of a capacitor to rise to 63% of its value when fully charged.
- It is equal to RC.
Derive the definition of the time constant, τ.
- When t = τ = RC,
- Q = Q₀e^(-t/RC) = Q₀e^-1
- So Q/Q₀ = e^-1 = 0.37
- Therefore, τ is the time for the charge of a fully charged capacitor to fall to 37% of its initial value.
In practice, how many time constants does it take for a capacitor to fully discharge?
About 5RC or 5τ.
How can you find the time constant, τ?
Either do τ = RC. or Read it from a Q-t or ln(Q)-t graph: Discharging: 0.37Q₀ Charging: 0.63Q₀
Remember to revise how τ is shown on a graph.
Pg 136 of revision guide
How can the time constant be found from a Q-t graph for a discharging capacitor?
- Look at the point at which the charge is 37% of the initial charge
- Find the time taken for the charge to fall to that charge
What graph can be plotted to find the time constant more accurately when discharging?
ln(Q) against t
NOTE: This also works with potential difference or current instead of charge
Derive which graph should be plotted to find the time constant more accurately when discharging.
- Q = Q₀e^(-t/RC)
- ln(Q) = (-1/RC)t + ln(Q₀)
- This is now in the form y = mx + c.
- Plot ln(Q) against t. The gradient is -1/RC.
(NOTE: This also works for potential difference and current instead of charge.)
What is the symbol for time to halve?
T(1/2)
Where 1/2 is in subscript.
What is time to halve, T(1/2)?
- The time taken for the charge, current or potential different of a discharging capacitor to reach half of the value when fully charged
- 0.69RC
What are the values to remember for the time constant (τ) and time to halve (T(1/2))?
Time constant:
• 0.37 of full charge when discharging
• 0.63 of full charge when charging
Time to halve:
• 0.69RC
What is the equation for time to halve, T(1/2)?
T(1/2) = 0.69RC
Where:
• T(1/2) = Time to halve (s)
• R = Resistance in the circuit (Ω)
• C = Capacitance (F)
Derive the equation for time to halve.
- We’re looking for the time when Q = 1/2 x Q₀
- So 1/2 x Q₀ = Q₀ x e^(-t/RC)
- 1/2 = e^(-t/RC)
- ln(1/2) = -t/RC
- ln(1) - ln(2) = -t/RC
- ln(2) = t/RC
- t = ln(2)RC
- t = 0.69RC
Remember to practice deriving the equations for the time constant and time to halve.
Pgs 136 and 137 of revision guide.
How can you tell if something is exponential decay?
It always takes the same length of time for the quantity to halve.
