Capacitance

Question 1

How does a capacitor work

Answer 1

Stores energy as electrostatic potential in electrostatic firefly
One time, quick transfer of energy
Device designed to store energy by storing charge

Question 2

What does it mean when a capacitor is said to store a total charge of Q

Answer 2

-Q charge on one plate and +Q charge in the other

Question 3

What is charge stored by a capacitor

Answer 3

Q = It
where I is constant

Question 4

Define the capacitance of a capacitor

Answer 4

Charge stored per unit p.d

Question 5

Capacitance formula

Answer 5

C = Q / V

C = capacitance
Q = charge stored
V = potential difference

Question 6

Define capacitance of a capacitor

Answer 6

Charge stored per unit potential difference across it.

Question 7

Charge stored in a capacitor is

Answer 7

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

Question 8

What are capacitors

Answer 8

Electrical components in which charge is separated. Consist of two metallic plates separated by an insulator, often known as a dielectric

Question 9

Describe how charge is stored in a capacitor

Answer 9

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

Question 10

What is capacitance measured in

Answer 10

Farads

Question 11

For any capacitor, the greater the amount of + and - charge stored on the 2 plates…

Answer 11

The greater the p.d across them

Charge on the capacitor is always proportional to the p.d

Question 12

For two or more capacitors in parallel

Answer 12

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 +…

Question 13

For two or more capacitors in series

Answer 13

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…

Question 14

Describe what happens when an electron moves towards the negative plate of a capacitor that is being charged

Answer 14

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

Question 15

Where does energy stored in a capacitor come from

Answer 15

The power supply or energy of the battery

Question 16

What can a p.d against charge graph be used to determine

Answer 16

Energy stored in a capacitor

Question 17

What is area under a p.d against charge graph

Answer 17

Work done

Question 18

How to calculate small amount of work done with a p.d against charge graph

Answer 18

change in work done = p.d x change in charge stored

where p.d does not change significantly

Question 19

How does a p.d across a capacitor discharging through a resistor decrease over time

Answer 19

Exponentially

Question 20

How to discharge a capacitor

Answer 20

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

Question 21

General relationship between p.d against time for a discharging capacitor

Answer 21

V = V0 e^-t/CR

Question 22

General relationship between current against time for a discharging capacitor

Answer 22

I = I0 e^-t/CR

Question 23

General relationship between charge against time for a discharging capacitor

Answer 23

Q = Q0 e^-t/CR

Question 24

Define the time constant for a discharging capacitor

Answer 24

Time taken for the potential difference / current / charge to decrease to e^-1 of its original value

Question 25

What is time constant of a capacitor-resistor circuit equal to

Answer 25

Product of capacitance and resistance

Question 26

Modelling Exponential decay procedure

Answer 26

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

Question 27

How to charge a capacitor

Answer 27

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

Question 28

Equations for charging capacitor

Answer 28

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)

Question 29

Important rules to use to analyse circuits where a capacitor is charged through a resistor

Answer 29

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

Question 30

When may a capacitor be used

Answer 30

To generate high-output power