Physics 1202 Circuits: Part 1

1
Physics 1202Circuits Part 1

• Electric Circuits an Application of Conservation
• Conservation of Charge
• Conservation of Energy
• Rate of Charge (Current)
• Rate of Energy (Power)
• Connection of Energy Transfer and Current

Chapter 21 sections 1, 2 (to eq 21.9), 5 - 9)
2
Physics 1202Circuits Part 1
Conservation of Money
Initial time
final time

• Electric Circuits an Application of Conservation
• Conservation of Charge
• Conservation of Energy
• Rate of Charge (Current)
• Rate of Energy (Power)
• Connection of Energy Transfer and Current

Bank Account A
Bank Account B
Minitial Minput - Moutput Mfinal
Minput - Moutput Mfinal - Minitial
DMtransfer DMsystem
If no connection to outside world
Minput 0
Moutput 0
Chapter 21 sections 1, 2 (to eq 21.9), 5 - 9)
Isolated system
DMtransfer 0 thus DMsystem 0
3
CONSERVATION OF MASS
Conservation of Money
System mi A
System mf B
Initial time
final time
Bank Account A
Bank Account B
final time
Initial time
mi min - mout mf
min - mout mf - mi
Minitial Minput - Moutput Mfinal
Dmtransfer Dmsystem
Minput - Moutput Mfinal - Minitial
DMtransfer DMsystem
If no connection to outside world
If 16 grams of oxygen combines completely with 2
grams of hydrogen to form water, how many grams
of water are made?
Minput 0
Moutput 0
Isolated system
DMtransfer 0 thus DMsystem 0
4
Lecture Question If 16 grams of oxygen are
combined with 4 grams of hydrogen to make water,
how much hydrogen is left over?

• 0 g
• 2 g
• 12 g
• 16 g
• 18 g
• 20 g
• Not enough information

5
CONSERVATION OF CHARGE
CONSERVATION OF MASS
System mi A
System mf B
System qi A
System qf B
final time
Initial time
Initial time
final time
mi min - mout mf
qi qin - qout qf
min - mout mf - mi
qin - qout qf - qi
Dmtransfer Dmsystem
Dqtransfer Dqsystem
If 16 grams of oxygen combines completely with 2
grams of hydrogen to form water, how many grams
of water are made?
If a capacitor is charged to 16 microcoulombs and
then connected to another uncharged capacitor.
10 minutes later the charge on the first
capacitor is measured to be 5 microcoulombs.
What is the charge on the second capacitor?
6
Conservation in Biological Systems
CONSERVATION OF CHARGE
Cellular Energy Pathways
System qi A
System qf B
Initial time
final time
qi qin - qout qf
qin - qout qf - qi
Dqtransfer Dqsystem
If a capacitor is charged to 16 microcoulombs and
then connected to another uncharged capacitor.
10 minutes later the charge on the first
capacitor is measured to be 5 microcoulombs.
What is the charge on the second capacitor?
7
Photosynthesis
Conservation in Biological Systems

• Conservation of mass
• Conservation of elements
• Conservation of charge
• Conservation of energy

Cellular Energy Pathways
http//www.ahpcc.unm.edu/aroberts/main/photosyn.h
tm
8
Plant Growth

• Conservation of mass
• Conservation of elements
• Conservation of charge
• Conservation of energy

When an organism grows, its mass increases.
This mass comes from some input of an equal
amount of mass.
Photosynthesis
Dmsystem Dmtransfer
After many years a tree grows from a sapling.
What is the element that makes up most of the
mass of the trunk? Where does it come from?
http//www.ahpcc.unm.edu/aroberts/main/photosyn.h
tm
9
After many years a tree grows from a sapling.
What is the element that makes up most of the
mass of the trunk?
1.

• hydrogen
• oxygen
• nitrogen
• carbon
• silicon
• dirt

10
After many years a tree grows from a sapling.
Where does most of the mass of the trunk come
from?

• Minerals in the soil
• Water from the soil
• Nitrogen from the soil
• Oxygen from the air
• Carbon dioxide from the air
• Nitrogen from the air
• Light from the sun.

11
Problem Chap. 21, 20
Plant Growth
After studying all night you fall asleep dreaming
about the environmental effects of greenhouse
gasses released into the atmosphere. Suddenly,
your alarm clock goes off. While waking up it
occurs to you that there are approximately 270
million people in the US and each one has an
electric alarm clock with a power rating of about
2.50 W. How many metric tons of coal are burned
each hour to operate these clocks? Coal fired
electric generating plants are, on the average,
25.0 efficient in delivering electricity and
coal yields 33.0 MJ/kg.
When an organism grows, its mass increases.
This mass comes from some input of an equal
amount of mass.
Dmsystem Dmtransfer
After many years a tree grows from a sapling.
What is the material of the trunk and where did
it come from?
12
Problem Chap. 21, 20

• How much power is used by all of the electric
  alarm clocks in the US?
• 675 W
• 675 J
• 6.75 x 106 W
• 6.75 x 106 J
• 6.75 x 108 W
• 6.75 x 108 W

After studying all night you fall asleep dreaming
about the environmental effects of greenhouse
gasses released into the atmosphere. Suddenly,
your alarm clock goes off. While waking up it
occurs to you that there are approximately 270
million people in the US and each one has an
electric alarm clock with a power rating of about
2.50 W. How many metric tons of coal are burned
each hour to operate these clocks? Coal fired
electric generating plants are, on the average,
25.0 efficient in delivering electricity and
coal yields 33.0 MJ/kg.
13
Focus the Problem
Problem Chap. 21, 20
2.50 W
After studying all night you fall asleep dreaming
about the environmental effects of greenhouse
gasses released into the atmosphere. Suddenly,
your alarm clock goes off. While waking up it
occurs to you that there are approximately 270
million people in the US and each one has an
electric alarm clock with a power rating of about
2.50 W. How many metric tons of coal are burned
each hour to operate these clocks? Coal fired
electric generating plants are, on the average,
25.0 efficient and coal yields 33.0 MJ/kg.
1 hr
Einput
270 x 106
Ecoal
Mcoal
Efficiency is 25.0
33.0 MJ/kg
Question
How much coal (in metric tons) is burned per hour
to run clocks?
Approach
Use conservation of energy
Ein - Eout Ef - Ei
System the clock
Clock energy does not change Ef Ei so Ein
Eout
Ein is the input power times time
Ein comes from the power station
Ein is only 25 of Ecoal
Ecoal is (33.0 MJ/kg)Mcoal
14
Physics Description
Focus to Problem
Diagram
2.50 W
Einput
1 hr
270 x 106
Ecoal
Mcoal
Efficiency is 25.0
33.0 MJ/kg
Pout 2.5 W x 270 x 106
Question
How much coal (in metric tons) is burned per hour
to run clocks?
e 0.250
Dt 1 hr
b 33.0 MJ/kg
Approach
Target quantity
Mcoal
Use conservation of energy
Ein - Eout Ef - Ei
System the clock
Conservation of energy
Clock energy does not change Ef Ei so Ein
Eout
Ein Eout
Plant efficiency
Ein is the input power times time
Ein comes from the power station
Clock Eout Pout Dt
Ein is only 25 of Ecoal
Ecoal b Mcoal
Ecoal is 33.0 MJ/kg Mcoal
15
Plan
Physics Description
unknowns
Diagram
Find
Mcoal
Mcoal
1
Ecoal
Find
Ecoal
Pout 2.5 W x 270 x 106
Ein
2
e 0.250
Dt 1 hr
b 33.0 MJ/kg
Find
Ein
Target quantity
Mcoal
Ein Eout
3
Eout
Conservation of energy
Find
Eout
Ein Eout
Eout Pout Dt
4
4 unknowns, 4 equations
Plant efficiency
Clock Eout Pout Dt
Ecoal b Mcoal
16
Execute
Plan
unknowns
Solve 4 for Eout
Find
Mcoal
Mcoal
Eout Pout Dt
Put into 3
1
Ecoal
Solve 3 for Ein
Find
Ecoal
Ein Pout Dt
Put into 2
Ein
2
Solve 2 for Ecoal
Find
Ein
Ein Eout
3
Eout
Put into 1
Find
Eout
Solve 1 for
Eout Pout Dt
4
4 unknowns, 4 equations
17
Check units
Execute
Solve 4 for Eout
Eout Pout Dt
Put into 3
Solve 3 for Ein
Correct for M
Put in numbers
Ein Pout Dt
Put into 2
Solve 2 for Ecoal
Put into 1
Solve 1 for
18
Evaluate
Check units
Correct for M
Is the answer unreasonable?
Put in numbers
1 cubic meter of water has a mass of one ton.
Coal is at least twice as dense as water so 300
tons of coal occupies about 150 cubic meters.
This is big but not an impossible pile of coal
divided among all the power plants in the
country.
Checking the behavior of the final equation.
The mass of coal per hour increases with the
power of the clock. Reasonable.
It also decreases if the efficiency of the power
plant increases. Reasonable.
19
Conservation and Electric Circuits
Evaluate
Is the question answered properly?
Yes the mass of coal in tons per hour was
calculated.
Study a simple version of a biological system
Is the answer unreasonable?
Ionic diffusion across membranes
1 cubic meter of coal has a mass of one ton.
Coal is at least twice as dense as water so 300
tons of coal occupies about 150 cubic meters.
This is not a huge pile of coal so it is not
unreasonable.
Nerve signal propagation
Heart beat regulation
Memory
Instrumentation
Checking the behavior of the final equation.
DNA separation using gels
Everything electrical in lab
Medical applications
The mass of coal per hour increases with the
power of the clock. Reasonable.
Non-invasive tests and treatment
It also decreases if the efficiency of the power
plant increases. Reasonable.
Heart regulation
20
Simple Circuits
Conservation and Electric Circuits
What determines the brightness?
Study a simple version of a biological system
Ionic diffusion across membranes
Nerve signal propagation
Heart beat regulation
What is necessary to light the bulb?
Memory
Battery (energy source) Bulb (energy output) A
return path (energy carriers)
Instrumentation
DNA separation using gels
Conservation of Energy
Everything electrical in lab
Ein - Eout Ef - Ei
Medical applications
System the bulb
Energy input?
Non-invasive tests and treatment
Energy output?
Does system energy change?
Heart regulation
21
Conservation of Energy
Simple Circuits
Where does the input energy come from?
Battery runs down.
How is energy delivered to the bulb?
Something carries the energy through the wire.
Objects with an electric charge (electrons)
What is necessary to light the bulb?
Battery (energy source) Bulb (energy output) A
return path (energy carriers)
Functioning of the Battery.
Chemical Energy
Conservation of Energy
Atomic processes
Ein - Eout Ef - Ei
Each electron gets the same energy
System the bulb
A battery delivers the same amount of energy for
each charge.
Energy input?
Energy output?
Does system energy change?
Fixed energy/charge called voltage
22
Conservation of Energy
Example Copper-Zinc Voltaic Cell (battery)
Where does the input energy come from?
Battery runs down.
At the anode (the side of battery) Zn
SO4-2 (soln) gt ZnSO4 (aq) 2e-
How is energy delivered to the bulb?
Something carries the energy through the wire.
The electron travels around circuit back to the
cathode (the side of battery)
Objects with an electric charge (electrons)
Functioning of the Battery.
Chemical Energy
At the cathode, 2e- CuSO4 (aq) gt Cu SO4-2
Atomic processes
Each electron gets the same energy
A battery delivers the same amount of energy for
each charge.
Fixed energy/charge called voltage
23
Each metal strip is in a solution of Sulfuric
Acid H2SO4 (aq)
What would happen if SO4-2 couldnt get through
membrane?
Zn SO4-2 (soln) gt ZnSO4 (aq) 2e-
2e- CuSO4 (aq) gt Cu SO4-2
Semi-permeable membrane
24
Conservation of Energy
Its a chemical reaction.
Where does the input energy come from?
We know from chemistry that the same amount of
energy is given off in a reaction each time.
This energy is carried by charges (in this case
it is electrons).
Battery runs down.
How is energy delivered to the bulb?
Something carries the energy through the wire.
Lets define something new then to quantify this
Objects with Electric Charge (electrons)
Functioning of the Battery.
Chemical Energy
Compare two 1.5 Volt batteries. Battery A has
been running a clock for a while. Battery B is
fresh. Which has more stored energy? Which has
more voltage?
Atomic processes
Each electron gets the same energy
A battery delivers the same amount of energy for
each charge.
Fixed energy/charge called voltage
25
Lecture Question Before it is put into a
circuit, what is the total charge of a battery?

• Zero
• Positive because current is positive
• Negative because electrons are negative
• Greater than zero
• Less than zero

26
Again, these next two are for fun
27
Before it is put into a circuit, what is the
total charge of the bulb?

• Zero
• Positive because current is positive
• Negative because electrons are negative
• Greater than zero
• Less than zero

28
Before it is put into a circuit, what is the
total charge of the wire?

• Zero
• Positive because current is positive
• Negative because electrons are negative
• Greater than zero
• Less than zero

29
Conservation of Charge
System the bulb
qin - qout qf - qi
Look back at the battery Whatever charge went
out of the battery came back in for the Chemical
Rx to take place.
Does system charge change?
Charge input?
Charge output?
Complete wire path needed so charge does not
build up.
Complete circuit
No charge build up
30
Lecture Question After it is connected into a
circuit, what is the total charge of a battery?

• Zero
• Positive because current is positive
• Negative because electrons are negative
• Greater than zero
• Less than zero

31
After it is connected into a circuit, what is the
total charge of the bulb?

• Zero
• Positive because current is positive
• Negative because electrons are negative
• Greater than zero
• Less than zero

32
After it is connected into a circuit, what is the
total charge of the wire?

• Zero
• Positive because current is positive
• Negative because electrons are negative
• Greater than zero
• Less than zero

33
Light
Conservation of Charge
System the bulb
A bulb lights when charge goes through it.
Does system charge change?
Energy is output
Charge input?
Each electron transfers some of its energy to the
bulb
Charge output?
Complete wire path needed so charge does not
build up.
The difference of energy per charge leaving the
battery and returning to the battery is always
the same.
Voltage difference DV
A brighter bulb means more energy is output in
the same time.
Complete circuit
Brightness is the rate of energy output.
No charge build up
Called Power
34
Power
Light
Bulb lights when charge goes through it.
Energy is output
Each charged object transfers some of its energy
to the bulb
Conservation of Energy
Ein - Eout Ef - Ei
The difference of energy per charge leaving the
battery and returning to the battery is always
the same.
System the bulb
If Ef Ei
Ein Eout
And
Voltage difference DV
Ein comes from the battery
A brighter bulb means more energy is output in
the same time.
Brightness is the rate of energy output.
Called Power
35
Definitions
Power
Brightness or Power out of bulb
Poutput
Is the rate charge goes through the bulb
Conservation of Energy
Ein - Eout Ef - Ei
System the bulb
Called the current
If Ef Ei
From conservation of energy and conservation of
charge
Ein Eout
And
Poutput IDV
Ein comes from the battery
Units of power called Watts
Units of energy called Joules
1 Watt 1 Joule/second
Units of current called Amps
Units of voltage called Volts
Voltage is also called Potential
36
Energy Transfer
Definitions
Brightness or Power out of bulb
As the charged object that carries the energy
goes around the circuit, it transfers energy at
specific sites in the circuit.
Poutput
Is the rate charge goes through the bulb
Called the current
From conservation of energy and conservation of
charge
Poutput IDV
Units of power called Watts
Units of energy called Joules
Need to know how much energy per charge (voltage)
is transferred at a site in an electrical circuit.
1 Watt 1 Joule/second
Units of current called Amps
Units of voltage called Volts
DV
Voltage is also called Potential
37
Energy Transfer per Charge
Energy Transfer
Eout
As the charged object that carries the energy
goes around the circuit, it transfers energy at
specific sites in the circuit.
Ein
Eout
Conservation of energy
System light bulb
Ef Ei Ein - Eout
Bulb energy does not change
Ein Eout Eout
Ein - Eout Eout
Vin - Vout Eout/q
Need to know how much energy per charge (voltage)
is transferred at a site in an electrical circuit.
Vout - Vin DV
How does the voltage change across a circuit
element depend on the current through that
element?
DV
38
Measurements
Energy Transfer per Charge
Eout
Some materials
(called resistors)
Ein
Linear behavior
Slope of line DV/I
Eout
R DV/I
Conservation of energy
Constant slope called Resistance
System light bulb
IR DV
Ohms Law
Ef Ei Ein - Eout
Bulb energy does not change
Other materials
Ein Eout Eout
Ein - Eout Eout
Vin - Vout Eout/q
Vout - Vin DV
How does the voltage change across a circuit
element depend on the current through that
element?
Slope of line not constant
No single Resistance, but they still have a
resistance
39
Objects that follow Ohms Law (called resistors)
are given the symbol
Objects that provide1 energy to a circuit (like a
battery) are given the symbol
R1
Example of a circuit diagram
R2
R3
1It is possible for a battery to absorb energy
from a circuit too. Think of a battery being
recharged
40
Summary
(1) Charge Conservation
While a circuit is running charge does not
accumulate at any part of a circuit. So,
whatever current goes in must come out.
Examples
Qin Qout
Battery
Qin
Qout
Bulb
Qin Qout
Qin
Qout
Wires
Qout_1
Qin Qout
Qin
Qout_1 Qout_2
Qout_2
Iin Iout
Lecture Question
41
Summary (contd)
(2) Energy is Conserved
Whatever energy the batteries give (or in some
cases, takes away think of a battery charger)
is outputted by other parts of the circuit
(bulbs, resistors, digital displays, etc..) as
the charges move around the circuit back to the
battery Voltage is related to energy Q(DV) E
More abstract way to look at it If you start at
some point (point a) in a circuit and go around
some path back to that same point (either Path A
or Path B), you must be at the same Voltage.
Why? Because energy is conserved and it is the
same point (Just like gravitational energy.) So
that means
R1
R2
a
R3