Physics 2CLLecture 2

"I am looking for a lot of men who have an infinite capacity to not know what can't be done."

--Henry Ford

RemarksLecture 1 – Resistors; errors; propagation of errors Background for Lab 01 (week 2 – this week)

Lecture 2 – CapacitanceBackground for Lab 02 (week 3 – next week)

No lecture on Monday, week 3 (University Holiday)

Address questions about Lab to Andrew Briggs,Lab TA Coordinator (LTAC): Discussion Board on TED, or email (see Syllabus)

For Lab 01 (week 2):– Read Lab 01 writeup (TED)– Read Chapters 1 and 2 of Taylor– Turn in Homework 1 (TED)– Reading quiz (lab writeup, text, lecture)– Academic Integrity Policy (TED)

CapacitanceWhat is capacitance?

Capacitance is the ability to hold charge. The more capacitance something has, the more capacity it has to hold charge.

What is a capacitor?

A capacitor is a device that stores charge when it is subjected to a potential difference.

What does a capacitor physically look like?

Although we represent most capacitors as two parallel plates, capacitors have a variety of shapes.

Capacitance

Camera flash

“Flash unit par 2”(Source: nakú)

http://www.flickr.com/photos/haiiroproject/4029196634/

Computer Keyboards

“Capacitor Applications”(Source: Thomson-Brooks Cole)

Serway & Jewett, Principles of Physics

Defibrillator“Philips HeartStart FR2 + AED”

(Source: Koninklijke Philips Electronics N.V.)http://www.alertfirstaid.com/FR2wECG.html

CapacitorsCapacitance, C, is a measure of how much charge can be stored for a capacitor with a given electric potential difference.

Where Q is the amount of charge on each plate (+Q on one, –Q on the other).

Capacitance is measured in Farads.

[Farad] = [Coulomb]/[Volt]

A Farad is a very large unit. Most things that you see are measured in μF or nF.

CapacitorsFor a parallel-plate capacitor, the capacitance is:

Here A is the area of one of the plates and d is the separation between the plates.

When you connect a battery to a capacitor, charge is pulled from one plate and transferred to the other plate.

CapacitorsThe transfer of charge will stop when the potential drop across the capacitor equals the potential difference of the battery.

Capacitance is a physical charac-teristic of the capacitor; the only way to change it is to change the geometry of the capacitor.

Thus, to increase capacitance, increase A or decrease d or make some other physical change to the capacitor.

DielectricsThe problem with capacitors is that they need to have huge dimensions to carry a significant amount of charge.Cost of material and manufacturing become a problem. The solution is to substitute an electrically insulating material between the parallel-plates instead of air or a vacuum.The material is known as a dielectric.When inserted into the capacitor, the dielectric will increase the overall capacitance.

DielectricsThe dielectric constant, κ, is the ratio of the new capacitance to the capacitance in a vacuum:

DielectricsEasily polarized materials have larger dielectric constants than materials not easily polarized.

DielectricsFilling a capacitor with a dielectric increases the capacitance by a factor equal to the dielectric constant.The capacitance for a parallel-plate capacitor changes to:

Common dielectric values:κvacuum = 1κair = 1.0006κglass ≈ 7Note that the dielectric constant is a unitless variable.

“MAKE presents: The Capacitor”(Source: makemagazine)

http://www.youtube.com/watch?v=ZYH9dGl4gUE

Teardown

CapacitorsWhat can you say about the potential difference between capacitors in parallel?

Capacitors in parallel all have the same potential differences.

What can you say about the equivalent capacitance of capacitors in parallel?

The equivalent capacitance of the parallel capacitors also will have the same potential difference.

They are additive:

CapacitorsWhat can you say about the charge stored on capacitors in series?Capacitors in series all have the same charge. What can you say about the equivalent capacitance of capacitors in series?

The equivalent capacitance of the series capacitors also will have the same amount of charge.

RC CircuitsWe have only had capacitors or resistors as our circuit elements, but what would happen if we had both?The simplest such circuit is:

What will happen when the switch is closed?A current will start to flow through the resistor and the capacitor will begin to charge.

Charges from one plate of the capacitor will flow to the other.

RC CircuitsWill the current be constant?

No, as more and more charge builds up, the current will slow down until it becomes zero.

This means that the current, I, is time dependent.

The charge, Q, on the capacitor plates will also be time dependent.

As time progresses, the charge will increase until it reaches some final value, Qf.

RC Circuits

This is a differential equation; the solution is (to find Q for a charging capacitor):

The capacitor charges exponentially as a function of time.

Perform a Kirchoff loop over the circuit to find Q.

∆VC: 0→max

Capacitor charging“Quick start“

––––

“Slow end“

IR: max→0

–+ –+–++–< >

RC CircuitsWe can also discharge the capacitor through a resistor.

This is a differential equation; the solution Q for a capacitor discharging is:

The charge decreases expo-nentially as a function of time as the capacitor discharges:

dQdt

R−QC= 0

RC CircuitsWhen the time t = τ ≡ RC (τ= time constant),

At time τ = RC, the charge in the capacitor decreases to 0.368 its maximum value.

In other words, in a time τ = RC, the capacitor loses 63.2% of its initial charge.

Time constant τ

τ = RC[s] [Ω][F]

RCτ + +

– –+ +– –

t = 0100.0%36.8%

∆VC: max→0

Capacitor discharging

IR: max→0

–

–

+

“Quick start““Slow end“

+

–

–

–

+–

+

–

–

< >

“100314-1150148”(Source: Waifer X)

http://www.flickr.com/photos/waiferx/4433948522/

(↓R)

Time constant τ↓

(↑R)

Time constant τ↑

“MAKE presents: The Capacitor”(Source: makemagazine)

http://www.youtube.com/watch?v=ZYH9dGl4gUE

“Capacitor explosion from excessive voltage”(Source: Gerald Walker, aka WallerMedia)

http://www.youtube.com/watch?v=_WheLp0RdLQ

Overloaded

Exercise Care When Handling Capacitors

“noccon01.flv”(Source: No-Contact LLC)

http://no-contact.com/index-2.html

Protective clothing

End