Physics of Technology PHYS 1800

Electric Circuits

Introduction Section 0 Lecture 1 Slide 1

Lecture 31 Slide 1

INTRODUCTION TO Modern Physics PHYX 2710

Fall 2004

Physics of Technology—PHYS 1800

Spring 2009

Physics of Technology

PHYS 1800

Lecture 31

Electric Circuits

Electric Circuits


Lecture 31 Slide 2


Fall 2004


Spring 2009

PHYSICS OF TECHNOLOGY Spring 2009 Assignment Sheet

*Homework Handout

PHYSICS OF TECHNOLOGY - PHYS 1800 ASSIGNMENT SHEET

Spring 2009 Date Day Lecture Chapter Homework Due Feb 16 17 18 19 20

M Tu W H F*

Presidents Day Angular Momentum (Virtual Monday) Review Test 2 Static Fluids, Pressure

No Class 8 5-8 5-8 9

-

Feb 23 25 27

M W F*

Flotation Fluids in Motion Temperature and Heat

9 9 10

6

Mar 2 4 6

M W F*

First Law of Thermodynamics Heat flow and Greenhouse Effect Climate Change

10 10 -

7

Mar 9-13 M-F Spring Break No Classes Mar 16 18 20

M W F*

Heat Engines Power and Refrigeration Electric Charge

11 11 12

8

Mar 23 25 26 27

M W H F*

Electric Fields and Electric Potential Review Test 3 Electric Circuits

12 13 9-12 13

-

Mar 30 Apr 1 3

M W F

Magnetic Force Review Electromagnets Motors and Generators

14 9-12 14

9

Apr 6 8 10

M W F*

Making Waves Sound Waves E-M Waves, Light and Color

15 15 16

10

Apr 13 15 17

M W F*

Mirrors and Reflections Refraction and Lenses Telescopes and Microscopes

17 17 17

11

Apr 20 22 24

M W F

Review Seeing Atoms The really BIG & the really small

1-17 18 (not on test) 21 (not on test)

No test week 12

May 1 F Final Exam: 09:30-11:20am * = Homework Handout

Electric Circuits


Lecture 31 Slide 3


Fall 2004


Spring 2009


PHYS 1800

Review

Lecture 31

Electric Circuits

Electric Circuits


Lecture 31 Slide 4


Fall 2004


Spring 2009

+q, -q charge mass m

wire pipe

switch valve

R resistor narrow pipe

I=(q/V)vA Charge flow rate (current)

Mass flow rate

(m/V)vA

q

PEV electric

Electric Circuits


Lecture 31 Slide 5


Fall 2004


Spring 2009

• Water flowing in a pipe is similar to electric current flowing in a circuit.– The battery is like the pump.– The electric charge is like the water.– The connecting wires are like the thick pipe.– The filament is like the nozzle or narrow pipe.– The switch is like the valve.

Electric Circuits


Lecture 31 Slide 6


Fall 2004


Spring 2009

• In a water-flow system, a high pressure difference will produce a large rate of water flow or current.– High pressure can be produced by raising the storage tank: this

pressure is related to the gravitational potential energy.– Likewise, a large difference in potential energy between the

charges at the two ends of a battery is associated with a high voltage and a greater tendency for charge to flow.

Electric Circuits


Lecture 31 Slide 7


Fall 2004


Spring 2009

Ohm’s Law and Resistance

• The electric current flowing through a given portion of a circuit is directly proportional to the voltage difference across that portion and inversely proportional to the resistance:

– Resistance R is the ratio of the voltage difference to the current for a given portion of a circuit, and is in units of ohms:

1 ohm = 1 = 1 V / A.– The resistance of a wire is proportional to the length of the wire,

inversely proportional to the cross-sectional area of the wire, and inversely proportional to the conductivity of the material.

R = L / (A σ)– It also depends on the temperature of the material.

Electric Circuits


Lecture 31 Slide 8


Fall 2004


Spring 2009

Series and Parallel Circuits

• In a series circuit, there are no points in the circuit where the current can branch into secondary loops.– All the elements line up on a single loop.– The current that passes through one element must also

pass through the others.

Electric Circuits


Lecture 31 Slide 9


Fall 2004


Spring 2009


PHYS 1800

Series Circuits

Lecture 31

Electric Circuits

Electric Circuits


Lecture 31 Slide 10


Fall 2004


Spring 2009

• In a series combination of resistances, each resistance contributes to restricting the flow of current around the loop.– The total series resistance of the combination Rseries is the sum

of the individual resistances:

– A common mistake is to think the current gets used up in

passing through the resistances in a series circuit.– The same current must pass through each component much

like the continuous flow of water in a pipe.

Series Circuits

Electric Circuits


Lecture 31 Slide 11


Fall 2004


Spring 2009

• It is the voltage that changes as the current flows through the circuit.– Voltage decreases by Ohm’s Law: V = I R

as the current passes through each resistor.• The total voltage difference across the combination is the

sum of these individual changes.– If two light bulbs are connected in series with a battery, the

current will be less than with a single bulb, because the total series resistance is larger.

– The bulbs will glow less brightly.

Series Circuits

Electric Circuits


Lecture 31 Slide 12


Fall 2004


Spring 2009

Two resistors are connected in series with a battery as shown. R1 is less than R2. Which of the two resistors

has the greater current flowing through it?

The current is the same in each, since it is a series circuit.

a) R1

b) R2

c) Bothd) Neither

Series Circuits

Electric Circuits


Lecture 31 Slide 13


Fall 2004


Spring 2009

Two resistors are connected in series with a battery as shown. R1 is less than R2. Which of the two resistors has the

greatest voltage difference across it?

The voltage difference is greater across R2. According to Ohm's Law, V = IR, so for the same current, the larger the resistance the greater the potential difference.

a) R1

b) R2

c) Bothd) Neither

Series Circuits

Electric Circuits


Lecture 31 Slide 14


Fall 2004


Spring 2009

In the circuit shown, the 1- resistance is the internal resistance of the battery and can be considered to be in series with the

battery and the 9- load. What is the current flowing through the 9- resistor?

a) 0.1 Ab) 0.3 Ac) 0.9 Ad) 3 Ae) 10 A

A 3.0 10

V 3

10 1 9

series

totalseries

series

R

VI

R

Series Circuits

Electric Circuits


Lecture 31 Slide 15


Fall 2004


Spring 2009

In the circuit shown, the 1- resistance is the internal resistance of the battery and can be considered to be in

series with the battery and the 9- load. What is the voltage across the 9- resistor?

a) 0.1 Vb) 0.3 Vc) 1.0 Vd) 2.7 Ve) 3.0 V

since I9 Iseries :

V9 IseriesR9 0.3 A 9 2.7 V

Series Circuits

Electric Circuits


Lecture 31 Slide 16


Fall 2004


Spring 2009

Three resistors are connected to a 6-V battery as shown. The internal resistance of the battery is negligible. What is the current through the 15-

resistance?

a) 0.1 Ab) 0.15 Ac) 0.4 Ad) 1.5 Ae) 4.0 A

Rseries 15 20 25 60

I15 Iseries Vtotal

Rseries

6 V

60 0.1 A

Series Circuits

Electric Circuits


Lecture 31 Slide 17


Fall 2004


Spring 2009

Does this same current flow through the 25- resistance?

a) Yes.b) No.c) It depends on

various things.

Yes. Since all the resistors are in series, the same current must flow through all three. There is no other path for the current through the 15- resistor to follow, except to go through the 20- resistor and then the 25- resistor.

Series Circuits

Electric Circuits


Lecture 31 Slide 18


Fall 2004


Spring 2009

What is the voltage difference across the 25- resistance?

a) 0.1 Vb) 2.5 Vc) 6 Vd) 25 Ve) 60 V

since I25 Iseries :

V25 IseriesR25 0.1 A 25 2.5 V

Series Circuits

Electric Circuits


Lecture 31 Slide 19


Fall 2004


Spring 2009


PHYS 1800

Parallel Circuits

Lecture 31

Electric Circuits

Electric Circuits


Lecture 31 Slide 20


Fall 2004


Spring 2009

• In a parallel circuit, there are points at which the current can branch or split up into different paths.– The flow divides and later rejoins.– The total cross-sectional area the current (or water) flows

through is increased, therefore decreasing the resistance to flow:

Parallel Circuits

Electric Circuits


Lecture 31 Slide 21


Fall 2004


Spring 2009

Parallel Circuits• In a parallel combination of resistances, the voltage

difference across each resistance is the same, since they are all connected between the same two points.– The currents can be different, since they divide: they add to give

the total current through the combination.– A portion of the total current flows through each branch.

Electric Circuits


Lecture 31 Slide 22


Fall 2004


Spring 2009

Two 10- light bulbs are connected in parallel to one another, and this combination is connected to a 6-V battery. What is

the total current flowing around the loop?

a) 0.6 A b) 1.2 A c) 6 A d) 12 A e) 60 A

Parallel Circuits

Electric Circuits


Lecture 31 Slide 23


Fall 2004


Spring 2009

How much current passes through each light bulb?

a) 0.6 A b) 1.2 A c) 6 A d) 12 A e) 60 A

Parallel Circuits

Electric Circuits


Lecture 31 Slide 24


Fall 2004


Spring 2009

Three identical resistors, each 24 , are connected in parallel with one another as shown. The combination is connected to

a 12-V battery whose internal resistance is negligible.What is the equivalent resistance of this parallel

combination?

a) 0.0417 b) 0.125 c) 8d) 24 e) 72

1

Rparallel

1

R1

1

R2

1

R3

1

24

1

24

1

24

3

24

1

8

Rparallel 8

Parallel Circuits

Electric Circuits


Lecture 31 Slide 25


Fall 2004


Spring 2009

What is the total current through the combination?

a) 0.5 Vb) 1.0 Vc) 1.2 Vd) 1.5 Ve) 12 V

Itotal Vtotal

Rparallel

12 V

8 1.5 V

Parallel Circuits

Electric Circuits


Lecture 31 Slide 26


Fall 2004


Spring 2009

How much current flows through each resistor in the combination?

a) 0.5 Vb) 1.0 Vc) 1.2 Vd) 1.5 Ve) 12 V

The resistors are identical and are in parallel,

so the same current must flow through each resistor.

The total current is plit into three identical parts:

Ione 24 - resistor 1

3Itotal

1

31.5 V 0.5 V

Parallel Circuits

Electric Circuits


Lecture 31 Slide 27


Fall 2004


Spring 2009

In the circuit shown, R3 is greater than R2, and R2 is greater

than R1. is the electromotive force of the battery whose internal resistance is negligible. Which of the three resistors

has the greatest current flowing through it?

R3 has the greatest current since the current in it is the sum of the currents in R1 and R2.

a) R1

b) R2

c) R3

d) R1 and R2 are equal, and greater than R3

e) They are all equal

Parallel Circuits

Electric Circuits


Lecture 31 Slide 28


Fall 2004


Spring 2009


PHYS 1800

Power in Electric Circuits

Lecture 31

Electric Circuits

Electric Circuits


Lecture 31 Slide 29


Fall 2004


Spring 2009

Electric Energy and Power

• Energy is supplied to a water-flow system by the pump, which increases the gravitational potential energy of the water by lifting it up to a higher tank.

• As the water flows down through pipes to a lower tank, gravitational potential energy is transformed into kinetic energy of the moving water.• Once the water comes to rest in the lower tank, the kinetic energy is dissipated by frictional or viscous forces which generate heat.

Electric Circuits


Lecture 31 Slide 30


Fall 2004


Spring 2009

• Similarly, in an electric circuit energy is supplied by a battery, which draws its energy from the potential energy stored in its chemical reactants.– The battery increases the potential energy of electric charges

as it moves positive charges toward the positive terminal and negative charges toward the negative terminal.

– When we provide an external conducting path from the positive to the negative terminal, charge flows from points of higher potential energy to points of lower potential energy.

• As potential energy is lost, kinetic energy is gained by the electrons.• This kinetic energy is converted to heat by collisions with other electrons and atoms.


Electric Circuits


Lecture 31 Slide 31


Fall 2004


Spring 2009

• Since voltage is potential energy per unit charge, multiplying a voltage difference by charge yields energy.

• Since current is the rate of flow of charge, multiplying a voltage difference by current yields power, the rate of energy use.

• The power supplied by a source must equal the power dissipated in the resistances.

Energy source potential energy kinetic energy heat

RII

RIRIRP

IRVVI

IP

2

2)(

;


Electric Circuits


Lecture 31 Slide 32


Fall 2004


Spring 2009

What is the power dissipated in a 20- light bulb powered by two 1.5-V batteries in series?

a) 0.15 Wb) 0.45 Wc) 3.0 Wd) 6.67 We) 60 W

1 2 3 V

R 20

IR

I R

3 V

20 0.15 A

P I I2R (0.15 A) 2(20 ) 0.45 W

check :

P I (3 V)(0.15 A) 0.45 W


Electric Circuits


Lecture 31 Slide 33


Fall 2004


Spring 2009

• The ease with which electric power can be transmitted over considerable distances is one of its main advantages over other forms of energy.– The source of the energy might be gravitational potential

energy of water, chemical potential energy stored in fossil fuels, or nuclear potential energy stored in uranium.

– Power plants all use electric generators that convert mechanical kinetic energy produced by turbines to electric energy.

– These generators are the source of the electromotive force.


Electric Circuits


Lecture 31 Slide 34


Fall 2004


Spring 2009

• The unit of energy commonly used to discuss electric energy is the kilowatt-hour, which is a unit of power (the kilowatt) multiplied by a unit of time (an hour).– 1 kilowatt equals 1000 watts– 1 hour = 3600 seconds– 1 kilowatt-hour equals 3.6 million joules

• The kilowatt-hour is a much larger unit of energy than the joule, but it is a convenient size for the amounts of electrical energy typically used in a home.


Electric Circuits


Lecture 31 Slide 35


Fall 2004


Spring 2009

How much does it cost to light a 100-watt light bulb for one day? Assume an average rate of cost of 10 cents per

kilowatt-hour.

a) 0.24 cents b) 2.4 cents c) 24 cents d) $2.40 e) $24

Energy used = power x time Cost = energy used x rate of cost = (100 W)(24 hr) = (2.4 kWh)(10 cents / kWh) = 2400 Wh = (2.4 kWh)(10 cents / kWh)

= 2.4 kWh = 24 cents


Electric Circuits


Lecture 31 Slide 36


Fall 2004


Spring 2009


PHYS 1800

Alternating Current and Household Wiring

Lecture 31

Electric Circuits

Electric Circuits


Lecture 31 Slide 37


Fall 2004


Spring 2009

Alternating Current and Household Circuits

• The current we draw from a wall outlet is alternating current (ac) rather than direct current (dc).– Direct current implies that the current flows in a single

direction from the positive terminal of a battery or power supply to the negative terminal

– Alternating current continually reverses its direction -- it flows first in one direction, then in the other, then back again.

– In North America the ac goes through 60 cycles each second (60 Hz).

Electric Circuits


Lecture 31 Slide 38


Fall 2004


Spring 2009

• The plot of electric current as a function of time for an alternating current is a sinusoidal curve.– The average value of an ordinary alternating current is zero.– The power dissipated in a resistance is proportional to the

square of the current.– The effective current or rms current is obtained by squaring

the current, averaging this value over time, and taking the square root of the result.

– The effective current Ieff is 0.707 times the peak current Ipeak.


Electric Circuits


Lecture 31 Slide 39


Fall 2004


Spring 2009

• If we plot the voltage across an electrical outlet as a function of time, we get another sinusoidal curve.– The effective value of this voltage is typically between 110 and

120 volts in North America.– The standard household power supplied in this country is 115

volts, 60 hertz ac.– Household circuits are wired in parallel so that different

appliances can be added to or removed from the circuit without affecting the voltage available.


Electric Circuits


Lecture 31 Slide 40


Fall 2004


Spring 2009

A 60-W light bulb is designed to operate on 120 V ac. What is the effective current drawn by the bulb?

a) 0.2 Ab) 0. 5 Ac) 2.0 Ad) 72 Ae) 7200 A

P 60 W

Veffective 120 V

P IV

I P

V

60 W

120 V

0.5 A


Electric Circuits


Lecture 31 Slide 41


Fall 2004


Spring 2009

• Household circuits are wired in parallel so that different appliances can be added to or removed from the circuit without affecting the voltage available.– As you add more appliances, the total current drawn

increases, because the total effective resistance of the circuit decreases when resistances are added in parallel.

– Since too large a current could cause the wires to overheat, a fuse or circuit breaker in series with one leg of the circuit will disrupt the circuit if the current gets too large.

– Appliances with larger power requirements (stoves, clothes dryers, etc) are usually connected to a separate 220-V line.


Electric Circuits


Lecture 31 Slide 42


Fall 2004


Spring 2009


Next Lab/Demo: Electric Circuits

Magnetism Thursday 1:30-2:45

ESLC 46 Ch 13 and 14

Next Class: Friday 10:30-11:20

BUS 318 roomRead Ch 14

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Physics of Technology PHYS 1800