M6, C1 Capacitors

Question 1

define capacitor

Answer 1

electrical components that can store electric charge

Question 2

what are capacitors made of

Answer 2

2 electrical conducting plates separated by a dielectric (insulating material)

Question 3

what is the circuit symbol for a capacitor

Answer 3

two parallel lines

must be same length

Question 4

What happens to the capacitor when it’s connected to a power source

Answer 4

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.

Question 5

Define capacitance

Answer 5

the capacitance of a capacitor is the amount of charge it is able to store per unit potential difference across it

Question 6

What do the parts of this equation mean:

C = Q/V

Answer 6

capacitance = charge / potential difference

Question 7

what is the units of capacitance

Answer 7

Farads (F)

Question 8

A 100µF capacitor is charged to a pd of 12V. How much charge is stored by the capacitor?

Answer 8

ALWAYS CONVERT THE MICROFARADS TO FARADS.

Q = CV
= 100X10^-6 X 12
= 1.2 X10^-3

Question 9

How is a negative charge built up on one of the plates of the capacitor?

Answer 9

The electrons flow from the negative terminal of the supply onto the plate connected to it.

Question 10

How is a positive charge built up on one of the plates of the capacitor?

Answer 10

Electrons flow from the other plate to the positive terminal of the supply. Making that plate less negative.

Question 11

What happens when the capacitor is fully charged

Answer 11

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.

Question 12

What is happening to the capacitor when it’s removed from the power source and it begins to discharge

Answer 12

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.

Question 13

draw a circuit diagram to show the action of a capacitor

which switches need to be open/closed when charging and discharging

Answer 13

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

Question 14

In the action of a capacitor why is there a resistor in the circuit?

Answer 14

to slow down the charging process

Question 15

derive the equation for the total capacitance when capacitors are in series

Answer 15

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…

Question 16

derive the equation for the total capacitance when capacitors are in parallel

Answer 16

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…

Question 17

On a charge-voltage graph, what does the area under the graph equal

Answer 17

the total energy stored by the capacitor

Explains why we have the equation W = 0.5QV

Question 18

derive the equations

W = 0.5V^2C and W = 0.5Q^2/C

Answer 18

Use W = 0.5QV

Sub in Q = CV and V = Q/C

Question 19

name some uses of the capacitor

Answer 19

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

Question 20

what does the gradient of a voltage-charge graph equal

Answer 20

1 / capacitance

Question 21

To model discharging capacitors with a spreadsheet, you need to find an equation which relates ∆Q and ∆t. Find this equation.

Answer 21

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)

Question 22

Outline the steps you would need to take to spreadsheet model a discharging capacitor.

Answer 22

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.

Question 23

For a discharging capacitor, draw a graph of

• current against time
• voltage against time
• charge against time

Answer 23

look them up

page 121 of year 2 textbook
page 137 of revision guide

Question 24

What does this equation mean

τ = CR

Answer 24

time constant = capacitance X resistance

Question 25

What does this equation mean

x = x_0e^(-t/CR)

Answer 25

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.

Question 26

What does this equation mean

x = x_0(1-e^(-t/CR))

Answer 26

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)

Question 27

What 2 factors does the time taken to charge or discharge a capacitor depend on?

Answer 27

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.

Question 28

For x = x_0e^(-t/CR), what happens when t = τ (time constant)

And therefore define time constant.

Answer 28

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.

Question 29

The larger the resistor in series with the capacitor, the _________ it takes to charge or discharge.

Answer 29

longer

Question 30

define time constant of a capacitor-resistor discharge circuit

Answer 30

The time taken for the p.d / current / charge to decrease to 1/e (37%) of its initial value.