6.1 Capacitors Flashcards
Capacitance
Charge stored per volt
Basic Equation for capacitance
C = Q/V
Structure of a capacitor
Two conductors separated by an insulator called a dieletric. Often rolled up to make it more compact.
Charging a capacitor (with reference to electrons)
When connected to a source of E.M.F. electrons will build up on the negative terminal of the capacitor. These electrons will then repel other electrons on the opposite plate, making it positively charged. As more electrons build up they repel further electrons from reaching the plate causing the current to decrease.
The P.D. over a fully charged capacitor
The same as that of the E.M.F
Discharging a capacitor (with reference to electrons)
Once the E.M.F is no longer being applied to the capacitor the electrons will flow from the negative plate through the wires.
How to experimentally measure capacitance
Set up a capacitance in series with an ammeter and a voltmeter around, along with a variable resistor. Turn on the power and adjust the variable resistor to keep the current the same (start it high). Regularly take readings for potential difference and current. Calculate charge at a given time by using Q = It. Plot a graph of Q against V and take the gradient of the line to be the capacitance. (Or you can use the final charger divided by the final voltage but this may be less reliable).
Measuring capacitance graphically
The gradient of a Q-V graph
Effective capacitance of multiple capacitors in parallel
C = C1 + C2 + C3…
Effective capacitance of multiple capacitors in series
1/C = 1/C1 + 1/C2 + 1/C3…
Energy stored by a capacitor from a graph
Area under a V-Q graph
Energy stored by a capacitor (basic equation)
E = (1/2)QV
Disadvantages of using capacitors as an energy store (2)
- Can’t store much energy
- Energy slowly leaks out
Examples of capacitors used as energy storage (3)
- Flash devices for cameras. A capacitor stores energy which is then released very quickly, exciting a gas and causing a brief flash.
- Back up energy supply. Large capacitors can be used for a short term supply of back up energy (long enough to safely shut down computers and ensure data is saved in the event of a power cut).
- Pulsed power in nuclear fusion research. Large capacitors output power at extremely high values. The power output of the Z machine is greater than that of all power stations on earth combined!
At what point in charging a capacitor will there be the greatest current
At the beginning
Shape of a graph of Q against t for charging
1 - (exponential decay)
Shape of a graph of Q against t for discharging
exponential decay
Shape of graph of I against t
exponential decay for both charging and discharging
Effect of resistance on charging/discharging a capacitor
Takes longer to charge / discharge. Stored current is unchanged.
Factors affecting time taken to charge a capacitor
resistance and capacitance
τ (tau)
Time constant.
= CR
The main feature of exponential decay
rate of change of quantity is proportional to the magnitude of the quantity at that time
What is τ practically
The time taken for the charge on a capacitor to fall to 1/e (37%) of its original value
Equation for exponential decay
x = (x0)*e^(-kt)
Experiment to investigate charging/discharging a capacitor
Set up a circuit with a resistor, ammeter/datalogger and capacitor with a voltmeter around the capacitor. Charge the capacitor by connecting wires and record current and voltage regularly. Connect up the wires so that the charge can be discharged through a resistor and record current and voltage regularly.
Charge on left plate = 5C
Charge on right plate = -5C
Charge on capacitor = ?
5C
Determing τ from a log graph
plotting a graph of t against lnQ will give a straight line in the form
lnQ = ln(Q0) - (t/CR)
therefore the gradient will be -1/(CR) = -1/τ
Determing τ from a Q-t graph
Take a tangent and the gradient of the tangent is -Q/CR
dQ/dt
-Q/CR
Testing if a graph is exponential decay
Check if time to half is constant
Exponential decay with a spreadsheet
Set initial values and then calculate using iteration.
dQ = dt(-Q/CR)
Two capacitors in series of 1F and 2F. Which one has a higher p.d. across it
the 1F one
Capacitors in series of 1F and 2F. How does the total charge stored relate to the charge stored at each capacitor
Charge stored overall is the same as at each capacitor
The two different ways to calculate charge stored on an individual capacitor in series
Total P.D * Total effective capacitance
P.D over that capacitor * capacitance of that capacitor
