Capacitance Flashcards
Define Capacitance
The charge stored (Q) by a capacitor per unit potential difference
How does a capacitor cause a uniform electric field
When 2 parallel metal plates are connected to a battery, (-ve) electrons from the battery go to one plate, making it (-ve) Then electrons leave the other plate and go to the battery making that plate (+ve) Opposite charges building up on the 2 parallel plates cause the field between them
What is a capacitor
An electrical component that stores charge Made up of 2 conducting parallel plates with a gap in between that may have a dielectric in
What is a dielectric
An insulating material that can be put between 2 conducting parallel plates to increase the ability of the capacitor to store charge
Define permittivity
Measure of the ability to store an electric field in the material
What does it mean for a capacitor to store charge
One conductor stores charge Q+ (Electrons that left it to go to the battery) and one conductor stores charge Q- (Electrons that came to it from the battery)
How does a dielectric increase the ability of a capacitor to store charge
When placed between the 2 plates, molecules in the dielectric become polarised.
So the side facing the positive plate becomes negatively charged, repelling more electrons from the positive plate, making it more positively charged.
The side facing the negative plate becomes positively charged, attracting more electrons to the negative plate, making it more negatively charged
What does it mean for molecules in a dielectric to become polarised
Dielectrics have polar molecules - one side positive, one side negative.
In no electric field, they are arranged in random directions
But in an electric field, they align themselves with the field
What is relative Permittivity Σr
How do you calculate it
Ratio of charged stored with the dielectric to charge stored without the dielectric
Q/Q0
Q0 - Charge stored without dielectric
OR
C/C0
C0 - Capacitance without dielectric
OR
Ratio of permittivity of dielectric to permittivity of free space
Σr=Σ/Σ0
How to calculate the capacitance of a capacitor with a dielectric in it
C = (Aεr ε0 )/d
εr ε0 = Permittivity of dielectric
How can one increase the capacitance of a capacitor that has a dielectric
Making the area of each plate larger
Decreasing the spacing of plates
Filling space with a dielectric with a large permittivty
What does a µ represent
x10-6
Why does a capacitor store energy
What form is this energy stored as
As work is done to force electrons onto 1 plate and off the other
Electric Potential Energy
How does potential difference across a capacitor change with charge stored
As potential difference is the energy per coulomb
P.d across a capacitor increases proportionally to the charge stored
What does the area under a Q-V graph represent
Energy stored in a capacitor
How to charge a capacitor
Connect it in a circuit with a power supply and resistor
I-t graph for a charging capacitor and its equation
I=I0e-(t/RC)
V-t graph for a charging capacitor and its equation
V=V0(1-e-(t/RC))
Q-t graph for a charging capacitor and its equation
What does the gradient represent
Current
Q=Q0(1-e-(t/RC))
Describe what happens when a capacitor is charging up
Current starts to flow and negative charge builds up on the plate connected to the negative terminal. of the cell.
On the opposite plate, electrons are repelled by the negative charge building up on the other (now increasing negative) plate
Therefore these electrons move to the positive terminal of the cell and an equal but opposite charge is formed on each plate, creating a potential difference.
As the charge across the plates increases, the potential difference increases but the electron flow decreases due to the force of electrostatic repulsion also increasing, therefore current decreases and eventually reaches zero.
How do you discharge a capacitor
Connect it to a closed circuit with just a resistor
I-t graph for a discharging capacitor and its equation
I=I0e-(t/RC)
V-t graph for a discharging capacitor and its equation
V=V0e-(t/RC)
Q-t graph for a discharging capacitor
Q=Q0e-(t/RC)
Why does current gradually decrease as a capacitor discharges
P.d across capacitor decreases gradually as it loses charge, V=IR
Also, the electrostatic force between electrons that repels them to each decreases as the number of electrons decreases
How do you show that a quantity changes exponentially
Show that the amount that it changes by each time changes by the same factor each time
Define the time constant
Time taken to discharge a capacitor to 37% of its initial charge
This value x5 gives you the time taken to (basically completely) discharge a capacitor to 99% of its original charge
How to calculate the time constant
RC
Time when the value is 0.37xthe initial Current/Voltage/Charge for a discharging capacitor
Time when the value is 0.63xthe initial Current/Voltage/Charge for a charging capacitor
How to calculate the time taken for Charge/Voltage/Current to half
Time constant x ln2
What happens to the energy stored in a charged capacitor that isn’t connected to a circuit when a dielectric is removed from it
Why?
Energy stored increases
In dielectric, polar molecules align in the field with positive end toward the negative plate
Work is done on the capacitor separating the positive surface of the dielectric from the negative plate
When a question asks for something when the ratio/% of charge/I/V to the original charge/I/V … is
eg. time taken for capacitor to discharge to 1% of its original charge
What is the best thing to do
Rearrange equations for charging/discharging
Q/Q0 = e-t/RC
