Capacitance Flashcards
How does a capacitor work
Stores energy as electrostatic potential in electrostatic firefly
One time, quick transfer of energy
Device designed to store energy by storing charge
What does it mean when a capacitor is said to store a total charge of Q
-Q charge on one plate and +Q charge in the other
What is charge stored by a capacitor
Q = It
where I is constant
Define the capacitance of a capacitor
Charge stored per unit p.d
Capacitance formula
C = Q / V
C = capacitance
Q = charge stored
V = potential difference
Define capacitance of a capacitor
Charge stored per unit potential difference across it.
Charge stored in a capacitor is
Directly proportional to the surface area of plates, A
Inversely proportional to distance between plates.
Dependent upon properties of dielectric between plates - permittivity of dielectric
What are capacitors
Electrical components in which charge is separated. Consist of two metallic plates separated by an insulator, often known as a dielectric
Describe how charge is stored in a capacitor
Electrons flow from the cell for a very short time. Electrons can not travel between the plates because of the insulation.
The very brief current means electrons are removed from plate A of the capacitor (the plate not connected to the cell) and at the same time electrons are deposited onto the other plate B (the plate connected to the cell)
Plate A becomes deficient in electrons and acquires a net positive charge. Plate B gains electrons and acquires a negative charge.
Current in the circuit must be the same at all points and charge must be conserved, so the two plates have an equal but opposite charge of magnitude Q.
This induces a potential difference across the plates.
Current in the circuit falls to zero when the p.d across the plates is equal to the e.m.f of the cell. The capacitor is then fully charged. Net charge on the capacitor plates is zero
What is capacitance measured in
Farads
For any capacitor, the greater the amount of + and - charge stored on the 2 plates…
The greater the p.d across them
Charge on the capacitor is always proportional to the p.d
For two or more capacitors in parallel
The potential difference across each capacitor is the same
Electrical Charge is conserved
Q total = Q1 + Q2 +…
Total capacitance is the sum of the individual capacitances in the capacitors
C total = C1 + C2 +…
For two or more capacitors in series
Kirchoff’s Second Law - Total p,d across the combination is the sum of the individual p.ds - V total = V1 + V2 +…
Charge Q stored by each capacitor is the same
The total capacitance is given by - 1 / C tot = 1 / C1 + 1/C2…
Describe what happens when an electron moves towards the negative plate of a capacitor that is being charged
Electron will experience a repulsive electrostatic force from all the electrons already on the plate. External work has to be done to push this electron onto the negative plate
Work is done to cause an electron to leave the positive plate of the capacitor
Work is provided by the power supply or energy of the battery
Where does energy stored in a capacitor come from
The power supply or energy of the battery
What can a p.d against charge graph be used to determine
Energy stored in a capacitor
What is area under a p.d against charge graph
Work done
How to calculate small amount of work done with a p.d against charge graph
change in work done = p.d x change in charge stored
where p.d does not change significantly
How does a p.d across a capacitor discharging through a resistor decrease over time
Exponentially
How to discharge a capacitor
Place a voltmeter in parallel to a resistor which is in parallel to a capacitance which is parallel to a battery with a closed switch in between the battery and capacitor
Open the switch
P.d across the capacitor or the resistor = V0
Current in resistor = V0 / R
Charge stored in the capacitor, Q = V0C
Capacitor discharges through the resistor, charge stored by the capacitor decreases with time so the p.d across it also decreases. Current in the resistor decreases with time as the p.d across it decreases accordingly
Eventually the p.d, charge stored by the capacitor and current in the resistor are all 0
General relationship between p.d against time for a discharging capacitor
V = V0 e^-t/CR
General relationship between current against time for a discharging capacitor
I = I0 e^-t/CR
General relationship between charge against time for a discharging capacitor
Q = Q0 e^-t/CR
Define the time constant for a discharging capacitor
Time taken for the potential difference / current / charge to decrease to e^-1 of its original value
What is time constant of a capacitor-resistor circuit equal to
Product of capacitance and resistance
Modelling Exponential decay procedure
I = V/R = Q / CR
I = negative change in Q / change in T
Change in Q / Change in T = negative Q / CR
Start with a known value for the initial charge and a known value for the time constant
Choose a time interval which is very small compared to the time constant
Calculate the charge leaving the capacitor in a time interval with the equation
change in Q = change in t / CR x Q
Calculate the charge Q left on the capacitor at the end of the period change in t by subtracting change in Q from the previous charge
Repeat the whole process for the subsequent multiples of the time interval change interval
How to charge a capacitor
Connect a capacitor in series to a switch, a battery and a resistor.
Battery provides a constant emf, capacitor has capacitance c and the resistance of the resistor is R.
The capacitor is initially uncharged and the switch is open
When the switch closes, current in the circuit is at a maximum and the capacitor starts to charge up.
The potential difference across the capacitor starts increases from zero as it gathers charge.
According to Kirchhoff’s second law, the p.d across the resistor and the p.d across the capacitor must always equal the e.m.f of the battery.
So the potential difference of the resistormust decrease as potential difference of the capacitor increases with time
After a long time depending on the time constant, the capacitor will be fully charged with a p.d equal to the emf of the battery and the p.d of the resistor will be zero. When this occurs, current in the circuit is zero
Equations for charging capacitor
Current decreases exponentially:
I = I0 x e^-t/cr
Voltage across the resistor decreases exponentially across time:
VR = V0 x e^-t/CR
Voltage across the capacitor:
VC= V0 - VR
or
VC = V0 (1-e^-t/CR)
Important rules to use to analyse circuits where a capacitor is charged through a resistor
V=IR for a resistor
Q=VC for a capacitor
Current in the circuit: I = I0 x e^-t/CR
Charge or p.d across the capacitor can be calculated with:urrent in the circuit: x = x0 x (1 - e^-t/CR)
V0 = VR +VC
When may a capacitor be used
To generate high-output power
