OBJECTIVE: 

I wil be able to calculate/determine:

1) Total voltage in a circut containing capacitors

2) Total capacitance in a circut containing capacitors

3) Total charge in a circut containing capacitors

4) Charge on EACH capacitor in a circuit containing capacitors

5) Voltage across each capacitor in a circuit containing capacitors

I will be able to calculate the capacitance for a capacitor filled with a dielectric after today's class

WORDS/FORMULAE FOR TODAY

TERMS:

• capacitor - two charged surfaces that can store electrical energy
• dielectric - "Dielectrics are insulators, plain and simple. The two words refer to the same class of materials, but are of different origin and are used preferentially in different contexts" taken from http://physics.info/dielectrics/

CONSTANTS:

• k_e = 8.987 x 10⁹ Nm²/C²
• k_e = 1/4πε_o

UNITS:

• Capacitance = C
  • (SI Units "farads" = F)
  • C = Q/∆V
  • farads are always positive
  • capacitance measures ability of the system to store charge
  • 1 farad is a MASSIVE amount of storage so we will typically talk in microfarads (μF = 10^-6 F) or picofarads (pF = 10^{-12 F})

FORMULAE:

• Capacitance:
  1. C = kε_oA/d (where k is the dielectric constant > 1)
  2. C = kC_o (capacitance increases when a dielectric is inserted)
  3. C = ε_oA/d (for a parallel plate capacitor)
  4. C = Q/∆V (generally)
• Electrical Field: For a parallel plate capacitor: E= σ/ε_o

WORK O' THE DAY: 

 

THIS is also a VERY good reference (for later, I'll sketch it out now)

C₁ = 1.0 f,  C₂ = 2.0 f, C₃ =  3.0 f

1) What is the total voltage present?

Answer: 12.0V

2) What is the total capacitance?

Answer: 1/2.0μf + 1/3.0μf + 1/4.0μf = so le 1.08 EE6 so let's 1/x that go get our total capacitance = 9.23 x 10^-7f

3) What is the total charge present?

Answer: C_total=Q_total/∆V_total so Q_t=C_t ∆V_t

= (9.23 x 10^-7f)(12.0V) = 1.11 x 10^-5C

4) Now let's learn how to calculate the charge on each capacitor!

Here's what you need to know, the total charge of the system (we calculated in #3) is the same as the charge on each cap in series.... so...:

There are 3 caps in series and the charge on each cap is the same as the TOTAL charge so:

Q_total = Q₁ = Q₂ = Q₃

So...

Q_total= 1.11 x 10^-5C (from #3) so each Q in series = 1.11 x 10^-5C

 

5) Now let's learn how to calculate the voltage across each capacitor!

Recall C₁ = Q₁/∆V₁

so ∆V₁ = Q₁/C₁

∆V₁ = 1.11 x 10^-5C/2.0μf = 5.54V

∆V₂ = 1.11 x 10^-5C/3.0μf = 3.70V

∆V₃ = 1.11 x 10^-5C/4.0μf = 2.78V

============================

TOTAL VOLTAGE = 12.0 Volts... which checks correctly

════════════════════

Now try one with your group.... pick values for several capacitors (make sure they are MICRO farads, you can outsmart yourselves otherwise) with either a 6.0 or a 12.0 V battery.

1) Total voltage in a circut containing capacitors

2) Total capacitance in a circut containing capacitors

3) Total charge in a circut containing capacitors

4) Charge on EACH capacitor in a circuit containing capacitors

5) Voltage across each capacitor in a circuit containing capacitors

 

Now insert a capacitor in paralell into the mix... how will you deal with THAT?

════════════════════

Now let's talk dielectrics.

A dielectric is an insulating material inserted between the two surfaces of a capacitor.... Take a moment to discuss with your group... what advantage might be gained by inserting an insulator between the plates of a paralell plate capacitor?

 

 

 

════════════════════

To quote from our good friends at physics.info (http://physics.info/dielectrics/):

Dielectrics in capacitors serve three purposes:

1. ".... allowing for smaller plate separations and therefore higher capacitances"

2. to increase the effective capacitance by reducing the electric field strength, which means you get the same charge at a lower voltage

3. to reduce the possibility of shorting out by sparking (more formally known as dielectric breakdown) during operation at high voltage.

Now take a few moments and be prepared to explain WHY and/or HOW each of those works...

Soooooo... that means we have a brand new equation:

• C = kε_oA/d (where k is the dielectric constant > 1)

take a look at the chart on page 791-- take a moment to note the definition of dielectric strength

Let's discuss...update your flashcards for capacitance now please

════════════════════

HOMEWORK:

• HW Problems 26, 43, 45, 47

Sorry for the crappy image quality -- school network was down so I'm at Starbucks had to use my phone/camera