PHYS2B - CapacitorLec

7/30/2019 PHYS2B - CapacitorLec

1/20

Physics 2BLecture 27A

"Success is the ability to go from one failure

to another with no loss of enthusiasm."

--Winston Churchill


2/20

Capacitors

Capacitors are usually used in circuits.A circuit is a collection of objects usuallycontaining a source of electrical energy (like a

battery).This energy source is connected to elements(like capacitors) that convert the electricalenergy to other forms.

We usually create a circuit diagram torepresent all of the elements at work in thereal circuit.


3/20

CircuitsFor example, lets say that we had

two capacitors connected in parallelto a battery.

In the circuit diagram we would

represent a capacitor with aparallel line symbol: ||

Also, in the circuit diagram wewould represent a battery with a

short line and a long line: i|

The short line representing thenegative terminal and the long line

representing the positive terminal.


4/20

CapacitorsThe previous real circuit

can then be drawn as acircuit diagram as follows:

In this circuit, both capacitorswould have the same potential

difference as the battery.

Vbat=V1=V2

Plus, we can say that the

charges on either plate areequal to the total that passesthrough the battery.

QTot=Q1+Q2


5/20

CapacitorsWe can essentially replace the

two capacitors in parallel withone equivalent capacitor (thismay make our life easier).

The equivalent capacitor musthave exactly the same externaleffect on the circuit as theoriginal capacitors.

The battery sees QTot passingthrough it and believes that theone equivalent capacitor has apotential difference ofV.


6/20

CapacitorsSo, to the battery the

equivalent capacitance is:

The equivalent capacitance of

capacitors in parallel is greaterthan the individual capacitors.

In general, for parallel capacitors:


7/20

CapacitorsWe can also have two

capacitors hooked upin series to a battery.

In this case thepotential differenceacross the battery isno longer equivalentto the potentialdifference acrosseither capacitor.But since the right C1 plate gets its negativecharges from the left C2 plate, we can say that

the charge on either capacitor must be the same.


8/20

CapacitorsThis means that the charge passing through the

battery is equivalent to the charge on eithercapacitor.

QTot=Q1=Q2

Also, the potential differenceacross either capacitor will sumto be the potential differenceacross the battery.

Vbat=V1+V2

We can essentially replace thetwo capacitors in series with

one equivalent capacitor.


9/20

CapacitorsThe battery sees QTot passing through it and

believes that the one equivalent capacitor has apotential difference ofVbat.

So, to the battery the equivalent capacitance is:

In general, for series capacitors:


10/20

CapacitorsRemember when you have multiple capacitors in acircuit that:

Capacitors in parallel all have the same potentialdifferences.

The equivalent capacitance of the parallelcapacitors also will have the same potentialdifference.

Capacitors in series all have the same charge.

The equivalent capacitor of the series capacitorsalso will have the same charge.


11/20

CapacitanceExample

Find the equivalent capacitancebetween points a and b in thegroup of capacitors connected inseries as shown in the figure tothe right (take C1=5.00F,C2=10.0F, and C3=2.00F). Ifthe potential between points aand b is 60.0V, what is thecharge stored on C3?

Answer

Reduce the circuit by equivalent capacitance to findQ3.

Start with the C1 and C2 in series on the top.


12/20

CapacitanceAnswer

Combine the two top capacitors thatare in series (left and right are thesame) to form an equivalent Cs:

Next, combine the top three that are in parallel:


13/20

CapacitanceAnswer

Finally, combine the remaining twocapacitors that are in series:

Next, combine the bottom two that are in parallel:


14/20

CapacitanceAnswer

Looking back at the two equivalent capacitors inseries (Cp1 and Cp2), we see that they must havethe same amount of charge:

Next, we need to find the total charge stored onthe equivalent capacitor:

This means that they potential difference across Cp1 is:


15/20

CapacitanceAnswer

We note that all three of thesecapacitors must have the samepotential difference as each other

(and Cp1).

We turn back to the three topcapacitors in parallel (CS, C3, and CS).

This means that the charge on

C3 is:


16/20

DielectricsThe problem with capacitors is that they need to

have huge dimensions to carry a significant amountof charge.

Cost of material and manufacturing become aproblem.

The solution is to substitute an electricallyinsulating material between the parallel-platesinstead of air or a vacuum.

This is known as a dielectric.

When inserted into the capacitor the dielectricwill increase the overall capacitance.


17/20

DielectricsThe dielectric constant, , is the ratio of the new

capacitance to the capacitance in a vacuum:


18/20

DielectricsEasily polarized materials have larger dielectric

constants than materials not easily polarized.


19/20

DielectricsFilling a capacitor with a dielectric increases the

capacitance by a factor equal to the dielectricconstant.The capacitance for a parallel-plate capacitorchanges to:

Common dielectric values:

vacuum=1

air=1.0006

glass 7

Note that the dielectric constant is a unitless

variable.


20/20

For Next Time (FNT)

Start reading Chapter 27

Keep working on the homework for

Chapter 26

Documents

PHYS2B - CapacitorLec