Today 3/28 Circuits

Current Potential (same as always) Capacitance (energy and in circuits)

HW: 3/28 “Circuits 3” Due Wednesday 4/2

Note: Watch out for “round off” errors,keep three decimal places to the end on all circuit homeworks.

Voltage Model

Voltage: how much energy each coulomb of charge gains (battery) or loses (bulb) in going through an element. (as usual)

More glow, more voltage. The Loop Rule:

What goes up, must come down! VA,A = 0,voltage rises and drops must must cancel around any loop.

Current Model Fails A

B

Compare B to D

B gets all of the current through A. D gets half of the current through C.

But the current through C is bigger than the current through A.

C

EDCan’t be sure which is brighter!!!

lesscurrent

morecurrent

all

1/21/2

Voltage ModelA

B

Compare B to D

C

ED

C brighter than DC has more voltage than D

VCVD

Compare the voltages across B and D. More volts more glow! Recall current for B and D.

VAVB

think loops

V

V

Voltage Model

The voltage for series elements SPLITS because it adds up to the battery voltage.

The voltage splits equally for identical Rs.

Otherwise, the voltage drop is greater across the greater R.

A

B

in series

Find Equivalent Resistance

12 V?

Req = 6

26

8 8

97

512 V 4

63

12

12

Find current through the battery

26

8 8

97

512 V

6

I = 2 Amps

12 V

It is the same as the current through Req.

Req = 6

Current through each element

26

8 8

97

512 V

6

I = 2 Amps

What is the current through each resistor?

12 V

1 Amp

1 Amp

0.5 Amp 0.5 Amp

0.25 Ampeach

What is the voltage across each resistor?

2 Amps

Voltage across each element

26

8 8

97

512 V

6

I = 2 Amps

What is the current through each resistor?

12 V 5 V

9 V

3 V 1 V

2 V each

What is the voltage across each resistor?

7 V

Kirchhoff’s Rules, Loop

The sum of all voltages around any closed loop is zero. (what goes up must come down) or VA,A = 0

!!must keep track of ups and downs!! (+/-)

Kirchhoff’s Rules, Junction

The sum of all currents at any junction is zero. (what goes in must come out) !!must keep track of ins and outs!! (+/-)

CapacitorsCapacitance tells me how many coulombs of charge are stored in a capacitor when it has 1 Volt across it.

A 25F capacitor will have 25C of charge on it when it has 1 volt across it. Think of capacitance as “coulombs per volt”.

Units: coulombs per volt or “Farads”Equation: C = q/V

CapacitorsThink of storing propane in a tank. The amount of propane depends on the pressure just as the amount of charge depends on voltage.

We will use parallel plate capacitors so that all ideas from parallel plates apply.

V = Ed E = /o (two plates) = Q/A

CapacitorsHow much charge is on the capacitor?

Think “6x10-6 Coulombs per Volt and you won’t need the equation!

12 V 6F

6F

72x10-6 C or 72C

CapacitorsWhat is the E-field inside the capacitor if the plates have an area of 1 m2?

12 V 6F

6F

Q = 72x10-6 C or 72C

E = /o = 8.2x106 N/C

What is the distance between the plates?

V = Ed d = 12/8.2x106 = 1.5x10-6 m

Note that capacitance depends on the area and separation distance

Capacitors and EnergyHow many Joules of energy are stored in the capacitor?

12 V 6F

Ask yourself, “How much work must be done to charge the plates?”

Capacitors and EnergyHow many Joules of energy are stored in the capacitor?

12 V 6F

As the battery moves charge from one plate to another, the potential difference increases from zero to 12 V. The average is 6 V and the energy stored is q times 6 V (qVave).

Energy = qVave = 1/2qV = 1/2CV2

C = q/V

Capacitors with ResistorsWill current flow when the switch is closed?

12 V

6F

6

12 V

6F

Yes, but only for an instant until the capacitor is charged.

Yes, but it will take longer to charge the capacitor.

Capacitors with ResistorsDescribe current and voltage long after the switch has been closed.

12 V

6F

6

12 V

6F

No current, 12 V across the capacitor.

No current, 12 V across the capacitor, zero V across the resistor.

Loop rule still applies!V = IR for resistors still applies!

Capacitors with ResistorsDescribe current and voltage long after the switch has been closed.

12 V

6F

22 Amps through the battery and both resistors.

4 V across 2 and 8 V across the capacitor and 4

Loop rule still applies!V = IR for resistors still applies!

4

Charging Capacitors in Series

The same amount of charge that enters one side of a capacitor, leaves the other.

Charging Capacitors in Series

The same amount of charge that enters one side of a capacitor, leaves the other.

Charging Capacitors in Series

The same amount of charge that enters one side of a capacitor, leaves the other.

Charging Capacitors in Series

The same amount of charge that enters one side of a capacitor, leaves the other.

Charging Capacitors in Series

The same amount of charge that enters one side of a capacitor, leaves the other.

Charging Capacitors in Series

The same amount of charge that enters one side of a capacitor, leaves the other.

Charging Capacitors in Series

The same amount of charge that enters one side of a capacitor, leaves the other.

Charging Capacitors in Series

The same amount of charge that enters one side of a capacitor, leaves the other. Capacitors in series

will always have the same charge on them. (what goes around, comes around)

This is true even if they are not of equal capacitance!

Current will flow until the sum of the voltages across the capacitors equals the battery voltage. (loop rule)

Capacitors in Series

Find the charge on each capacitor and the voltage across each capacitor. The battery is 30V.

25F

50F

They are in series so the charge on each is the same.Capacitance means “coulombs per volt” so the one with twice the capacitance has half the volts.

V

QC

1

2

V1 = 20V, V2 = 10V, Q1 = 500C, Q2 = 500C

Capacitors in Parallel

Find the charge on each capacitor and the voltage across each capacitor. The battery is 30V.

They are in parallel so the voltage across each is the same, each equal to 30V.

V

QC

Q1 = 750C, Q2 = 1500C

25F 50F

1 2

Series and Parallel

Objects in series have the same current through them. This is why capacitors in series always have the same charge on them.

Objects in parallel have the same voltage across them.

Ohm’s law, loops & junctions

V = IR true for entire circuits as well as individual elements.

Voltage changes summed around any closed loop equal zero.

Current divides and combines at junctions like water in pipes. What enters the junction must also leave.

Homework

R1=20100

R1=20

30F

15V