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Physics 132: Lecture 8ys cs 3 ectu e 8Elements of Physics II

A d f T dAgenda for Today Resistance Resistors Series Parallel

Ohm’s lawElectric Circuits Electric Circuits Current Kirchhoff’s laws

Physics 201: Lecture 1, Pg 1

Kirchhoff s laws

Stored energy in a capacitorFirst electron: W = q V = q (0)

QVU 1Last electron: W = q V q V

Average: W = 1/2 q VQVU 2

1Using Q = CV

- +- +- +

+Q-Q U = ½QV = ½CV2 = ½Q2/C

- +

- +- +

Battery


y

Clicker Question 1: A parallel plate capacitor is charged by connecting it to a

battery. The battery is then removed, leaving the charge on the capacitor plates. What happens to the energy stored in the capacitor when the plates are pulled a small distance further apart?

(a) It decreases . (b) It stays the same(c) It increases(c) It increases.


Electromotive force

Electromotive force (emf) is the maximum Electromotive force (emf) is the maximum potential difference a battery or power source can give a circuit. A b h f f 12 V A car battery has an emf of 12 V

Sometimes shown as a script (E)

Symbol for emf

-+


Electrical Current

When we connect the two terminals of an emf to When we connect the two terminals of an emf to a circuit ( a continuous conducting path), charge will move continuously through the circuit.

Since there is a potential difference electrons in circuit will feel a force

Electrons will flow in direction of positive

terminal

emf Battery “pushes”

electrons


Electrical Current

This flow is called electric current This flow is called electric current Net amount of charge through a point in the

circuit per unit time.

Units Ampere = Coulomb/second

qtq I


ExampleThe electron drift speed in a wire is exceedingly

slow-typically only a fraction of a millimeter per second. Yet when you turn on a flashlight switch, the light comes on almost instantly. Resolve this apparent paradox.


ExampleThe electron drift speed in a wire is exceedingly slow-typically p g y yp y

only a fraction of a millimeter per second. Yet when you turn on a flashlight switch, the light comes on almost instantly. Resolve this apparent paradox.pp p

Correct:It's like water analogy on page 877. as water (electrons) start flowing intoIt s like water analogy on page 877. as water (electrons) start flowing into

one end of the pipe(wire), water(electron) from the other end of pipe (wire) start turning paddle wheel immediately. therefore light can come instantly as

you turn on the switch.y

There is a line of electrons in the wire. That means the electrons are right next to each other, so as soon as you turn the flashlight on, electrons will start to move, but there is an electron already there behind the part that

produces the light so as electrons are added from the electrical current, the light is produced immediately.


Clicker Question 1:When a light bulb is emitting light in a circuit as g g g

below the number of electrons entering the light bulb is:(a) larger than the number leaving the light bulb(a) larger than the number leaving the light bulb(b) equal to the number leaving the light bulb(c) smaller than the number leaving the light bulb


Plinko Disks = electrons Disk bounces through

atoms on it’s way down theatoms on it’s way down the incline

Angle of incline = emfg(potential difference)

Y t b d Youtube demo


Resistance Resistance: Traveling through a conductor, electrons bump into

things which slows them downthings which slows them down. : Resistivity: Density of bumps L: Length of conductor

ALρR

A: Cross sectional area of conductor

A

Aρ

A All electrical devices will resist the flow

of electrical current

L


PlinkoALρR A


Clicker Question 2:

Iskinny

Below we have a skinny wire and a thick wire connected to identical batteries. Which case will have the larger current?

(a) Thick Wire( )(b) Skinny Wire(c) They will have the same current Ithick


Current must be the same in all t f l d l !parts of a closed loop!

Current must be the same in all parts of a closed loop! If not electrons will bunch up at a certain point, this will resist flow

of more electrons. The system will naturally make the current constant.

The current will reach an equilibrium


Student: when is the conductor in equilibrium and when is it not in equilibrium?

Superconductivity

This complete loss of resistance This complete loss of resistance at low temperatures is called superconductivity.

Superconductors have unusual magnetic properties. Here a g p psmall permanent magnet levitates above a disk of the high temperature superconductor p pYBa2Cu3O7 that has been cooled to liquid-nitrogen temperature.


Electric Current The direction of current flow – from the positive terminal to

the negative one – was decided before it was realized that electrons are negatively charged Therefore current flowselectrons are negatively charged. Therefore, current flows around a circuit in the direction a positive charge would move; electrons move the other way. However, this does not matter in most circuitsnot matter in most circuits.


Ohm’s law

With conductors the more resistance the less With conductors the more resistance the less current can flow

IRV Ohm’s law

• Hi h i t l t

IRV VI• Higher resistance lower current

Units are Ohms () RI


Resistor

A device that resists current A device that resists current

Used to control current flow in a circuitUsed o co o cu e o a c cu

Resistor in a circuit:

Generally in a circuit the resistance of the connecting wires are very small and we canconnecting wires are very small and we can neglect them. Wires will resist current, but we will assume they have zero


resistance!!

LRResistorALρR

Generally in a circuit the resistance of the connecting wires are very small and we can neglect them.

Student: How come the resistance of a wire is very very small, considering wires are usually longer than they are wide, so the Length is greater than the Area – shouldn’t the resistance be large?

Student: The textbook says about an ideal wire, but I don't understand how it i bl t t t if lt 0 Th kis possble to create a current if voltage = 0. Thanks


Kirchhoff’s Loop LawKirchhoff s Loop Lawfor the Simplest Circuit in the World

R

I

R• Example

Calculate I when emf =24 Volts and R = 8 – Calculate I when emf =24 Volts and R = 8 – Ohm’s Law: V=IR

I 24/8 3 Amps– I = 24/8 = 3 Amps


Clicker Question 5:Below we have two circuits, with identical batteries and three identical

Ccylindrical conductors. Compare the current in the two circuits:(a) IA > IB

(b) IA = IB

(c) IA < IB


Circuit A Circuit B

Clicker Question 6: A light bulb is connected to a battery in case A.

In case B an identical light bulb is added inIn case B an identical light bulb is added in series. What happens to the brightness of the original bulb?(a) it stays the same(a) it stays the same(b) it decreases(c) it increases


Case A Case B

Series wiring When two objects are connected end to end in a circuit, they are

id t b i isaid to be in series. Here R1 and R2 are in series

R1R2

Current must be same in each resistor!!

Voltage drop across R1 plus Voltage drop across R2should equal the emf of the battery


should equal the emf of the battery

Resistors in series One wire:

If charge goes through one resistor, it must go through other.

I1 = I2 = IeqV V V V1 + V2 = Veq

Add Req = R1 + R2 Adding Voltage IR + IR =I(R + R ) R1 Adding Voltage IR1 + IR2=I(R1 + R2) Adding length Req=(L1+L2)/A

1

R2

Req

2

The equivalent resistance of resistors in series is just the addition of the resistors


the addition of the resistors

Clicker Question 7:In the circuit below, what is the voltage across R1?

a) 12 VR = 4 R = 2 b) zero

c) 6 V

R1 = 4 R2 = 2

d) 8 V

e) 4 V 12 V


Clicker Question 7:In the circuit below, what is the voltage across R1?

R1 = 4 R2 = 2 R1 4 R2 2

12 V


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