Capacitance Flashcards
What is relative permittivity (Dielectric constant) ?
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
What does the area beneath a charge against Potential difference graph represent?
The electric potential energy stored by the capacitor
Describe a Q against T graph for the discharging of a capacitor through a resistor
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.
Describe a V against T graph for the discharging of a capacitor through a resistor
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.
Describe a I against T graph for the discharging of a capacitor through a resistor
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.
Describe a Q against T Graph for the charging of a capacitor through a resistor
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.
Describe a V against T Graph for the charging of a capacitor through a resistor
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.
What is the Time constant
The time it take for the change in the capacitor to fall to 1/e or 37% of the initial value
After how many time constants is a capacitor considered ‘Fully Discharged’
5
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
V = (Initial V)*e^(-t/RC)
As current and voltage are directly proportional
therefore
I = (Initial I)*e^(-t/rC)
What is the equation for the amount of the potential difference between the plates, when a capacitor is Charging
V = (Initial V)* ( 1 - e^(-t/RC) )
How does a capacitor Charge up? (6)
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
State 3 expressions for the energy stored by a capacitor
E = 1/2 * (Q^2 / C )
E = 1/2 * QV
E = 1/2 * CV^2
What 2 factors affect the time take for a capacitor to charge or discharge
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
What is Capacitance
The amount of charged stored per unit volt in a device or capacitor
Explain why a larger plate will store more charge, have a larger capacitance
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
What are Dielectrics?
How do they improve the performance of a capacitor?
- 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
How do dielectrics increase the capacitance of a capacitor (5)
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
How does a capacitor store electrical potential energy
although capacitor remains neutral and no net charge is stored
the difference in opposite charge creates an electric field
How do you calculate the time taken for a capacitor to charge to a certain charge
1) use Q = (initial Q) * (1-e^(-t/RC)
2) sub (initial Q) in for Capacitance * Peak Voltage
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
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)
constant angular velocity
constant decrease in area between plates
constant decrease in capacitance
What is the Half time of a Capacitor
Time Constant * ln(2)
B
C
State two factors of a capacitors design that affect its performance
Area of overlap between capacitor plates
Distance between the Capacitor plates.
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.
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
Describe how the potential differences across the resistor and capacitor change over time while the circuit is charging and discharging
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
Describe the energy changes that take place in the circuit in charging and discharging
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
State and explain whether capacitors B has a Larger or Smaller Capacitance then A
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
Explain what is meant by a dielectric constant of 6
The permitting it’s of the dielectric is 6 times the permittivity of free space
