6.1 Capacitors

Question 1

Capacitance

Answer 1

Charge stored per volt

Question 2

Basic Equation for capacitance

Answer 2

C = Q/V

Question 3

Structure of a capacitor

Answer 3

Two conductors separated by an insulator called a dieletric. Often rolled up to make it more compact.

Question 4

Charging a capacitor (with reference to electrons)

Answer 4

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.

Question 5

The P.D. over a fully charged capacitor

Answer 5

The same as that of the E.M.F

Question 6

Discharging a capacitor (with reference to electrons)

Answer 6

Once the E.M.F is no longer being applied to the capacitor the electrons will flow from the negative plate through the wires.

Question 7

How to experimentally measure capacitance

Answer 7

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).

Question 8

Measuring capacitance graphically

Answer 8

The gradient of a Q-V graph

Question 9

Effective capacitance of multiple capacitors in parallel

Answer 9

C = C1 + C2 + C3…

Question 10

Effective capacitance of multiple capacitors in series

Answer 10

1/C = 1/C1 + 1/C2 + 1/C3…

Question 11

Energy stored by a capacitor from a graph

Answer 11

Area under a V-Q graph

Question 12

Energy stored by a capacitor (basic equation)

Answer 12

E = (1/2)QV

Question 13

Disadvantages of using capacitors as an energy store (2)

Answer 13

• Can’t store much energy

- Energy slowly leaks out

Question 14

Examples of capacitors used as energy storage (3)

Answer 14

• 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!

Question 15

At what point in charging a capacitor will there be the greatest current

Answer 15

At the beginning

Question 16

Shape of a graph of Q against t for charging

Answer 16

1 - (exponential decay)

Question 17

Shape of a graph of Q against t for discharging

Answer 17

exponential decay

Question 18

Shape of graph of I against t

Answer 18

exponential decay for both charging and discharging

Question 19

Effect of resistance on charging/discharging a capacitor

Answer 19

Takes longer to charge / discharge. Stored current is unchanged.

Question 20

Factors affecting time taken to charge a capacitor

Answer 20

resistance and capacitance

Question 21

τ (tau)

Answer 21

Time constant.

= CR

Question 22

The main feature of exponential decay

Answer 22

rate of change of quantity is proportional to the magnitude of the quantity at that time

Question 23

What is τ practically

Answer 23

The time taken for the charge on a capacitor to fall to 1/e (37%) of its original value

Question 24

Equation for exponential decay

Answer 24

x = (x0)*e^(-kt)

Question 25

Experiment to investigate charging/discharging a capacitor

Answer 25

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.

Question 26

Charge on left plate = 5C
Charge on right plate = -5C
Charge on capacitor = ?

Answer 26

5C

Question 27

Determing τ from a log graph

Answer 27

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

Question 28

Determing τ from a Q-t graph

Answer 28

Take a tangent and the gradient of the tangent is -Q/CR

Question 29

dQ/dt

Answer 29

-Q/CR

Question 30

Testing if a graph is exponential decay

Answer 30

Check if time to half is constant

Question 31

Exponential decay with a spreadsheet

Answer 31

Set initial values and then calculate using iteration.

dQ = dt(-Q/CR)

Question 32

Two capacitors in series of 1F and 2F. Which one has a higher p.d. across it

Answer 32

the 1F one

Question 33

Capacitors in series of 1F and 2F. How does the total charge stored relate to the charge stored at each capacitor

Answer 33

Charge stored overall is the same as at each capacitor

Question 34

The two different ways to calculate charge stored on an individual capacitor in series

Answer 34

Total P.D * Total effective capacitance

P.D over that capacitor * capacitance of that capacitor