M6, C1 Capacitors Flashcards
define capacitor
electrical components that can store electric charge
what are capacitors made of
2 electrical conducting plates separated by a dielectric (insulating material)
what is the circuit symbol for a capacitor
two parallel lines
must be same length
What happens to the capacitor when it’s connected to a power source
Charge builds up on the plates.
One plate becomes negatively charged and one becomes positively charged.
No charge can move between the insulator.
This means that a pd builds up between the plates of the capacitor.
Creates a uniform electric field between the 2 plates.
Define capacitance
the capacitance of a capacitor is the amount of charge it is able to store per unit potential difference across it
What do the parts of this equation mean:
C = Q/V
capacitance = charge / potential difference
what is the units of capacitance
Farads (F)
A 100µF capacitor is charged to a pd of 12V. How much charge is stored by the capacitor?
ALWAYS CONVERT THE MICROFARADS TO FARADS.
Q = CV
= 100X10^-6 X 12
= 1.2 X10^-3
How is a negative charge built up on one of the plates of the capacitor?
The electrons flow from the negative terminal of the supply onto the plate connected to it.
How is a positive charge built up on one of the plates of the capacitor?
Electrons flow from the other plate to the positive terminal of the supply. Making that plate less negative.
What happens when the capacitor is fully charged
As charge builds up on 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 pd across the supply, the current falls to 0.
What is happening to the capacitor when it’s removed from the power source and it begins to discharge
The capacitor becomes the circuit’s source of emf.
A current flows around the circuit in the opposite direction to the charging current as the electrons from the negatively charged plate drift towards the positively charged plate through the circuit.
There is a strong force of repulsion between the electrons on the negative plate which pushes them away from the negative plate.
There’s also a strong force of attraction from the positive plate pulling electrons through the circuit towards the positive plate.
As electrons reach the positive plate, the pd decreases so current decreases.
When the pd and charge on each plate = 0 the capacitor is fully discharged.
draw a circuit diagram to show the action of a capacitor
which switches need to be open/closed when charging and discharging
look it up
(there’s a voltage supply, ammeter, capacitor, voltmeter, resistor, 2 switches)
to charge: switch 1 closed, switch 2 open
to discharge: switch 1 open, switch 2 closed
In the action of a capacitor why is there a resistor in the circuit?
to slow down the charging process
derive the equation for the total capacitance when capacitors are in series
For capacitors in series:
- pd is shared
- charge is the same
total pd = pd 1 + pd 2
V = Q/C therefore
total charge/total capacitance = Q1/C1 + Q2/C2
but Q is the same therefore
1/Ctotal = 1/C1 + 1/C2…
derive the equation for the total capacitance when capacitors are in parallel
for capacitors in parallel:
- pd is the same
- charge is shared
total charge = Q1 + Q2
Q = VC therefore
CtotalVtotal = C1V1 + C2V2
But V is the same. total V = V1 = V2 for parallel
therefore
total C = C1 + C2…
On a charge-voltage graph, what does the area under the graph equal
the total energy stored by the capacitor
Explains why we have the equation W = 0.5QV
derive the equations
W = 0.5V^2C and W = 0.5Q^2/C
Use W = 0.5QV
Sub in Q = CV and V = Q/C
name some uses of the capacitor
flash photography - the capacitor discharges really quickly to create a bright flash
back-up power supplies - eg. computers when not plugged in
smoothing out pd - maintain constant output
what does the gradient of a voltage-charge graph equal
1 / capacitance
To model discharging capacitors with a spreadsheet, you need to find an equation which relates ∆Q and ∆t. Find this equation.
I = ∆Q / ∆t and I = V / R
∆Q/∆t = V/R
V = Q/C
∆Q/∆t = -Q / RC
∆Q = -Q∆t / RC
(NOTE: it’s negative Q because it is discharging. You don’t need to include the minus when doing calculations)
Outline the steps you would need to take to spreadsheet model a discharging capacitor.
1) Create a table with 3 columns: time, change in charge and charge remaining.
2) Choose an initial starting charge for the capacitor along with a value of capacitance and resistance of the resistor.
3) Choose a sensible time interval that is significantly less than CR.
4) In the first row, t = 0 and Q = 0. ∆Q is blank.
5) In the next row:
t = t_0 + ∆t
∆Q = -Q∆t / RC
Q = Q_0 + ∆Q from previous row
6) Repeat this process of calculating the values in each row from Q and t in the row above.
7) Plot a graph of charge against time.
For a discharging capacitor, draw a graph of
- current against time
- voltage against time
- charge against time
look them up
page 121 of year 2 textbook
page 137 of revision guide
What does this equation mean
τ = CR
time constant = capacitance X resistance
What does this equation mean
x = x_0e^(-t/CR)
This equation is for a DISCHARGING capacitor.
t= time
C=capacitance
R=resistance
Can substitute charge, current or voltage in for x
They all decrease exponentially as the capacitor discharges.
It always takes the same length of time for the charge/voltage/current to halve no matter what you start with.
What does this equation mean
x = x_0(1-e^(-t/CR))
This equation is for a CHARGING capacitor.
t= time
C=capacitance
R=resistance
Can substitute charge or voltage in for x.
CANNOT substitute current in for x because it decreases exponentially still (only travelling in the opposite direction)
What 2 factors does the time taken to charge or discharge a capacitor depend on?
The capacitance because this affects the amount of charge that can be transferred at a given voltage.
The resistance of the circuit because this affects the current in the circuit.
For x = x_0e^(-t/CR), what happens when t = τ (time constant)
And therefore define time constant.
When you sub it in you will get,
x = x_0e^-1
x/x_0 = 1/e
= 0.37
Therefore the time constant is the time taken for the charge, potential difference or current on a discharging capacitor to fall to 37% of its initial value.
OR
the time taken for the charge or pd of a charging capacitor to rise to 63% of its maximum value.
The larger the resistor in series with the capacitor, the _________ it takes to charge or discharge.
longer
define time constant of a capacitor-resistor discharge circuit
The time taken for the p.d / current / charge to decrease to 1/e (37%) of its initial value.
