ELECTRIC CIRCUIT, ELECTRIC CURRENT, OHM's LAW
lab electricity 1: introduction circuits, Ohm's law INDEX CARD
PART I: INTRODUCTION: PRODUCING ELECTRIC CURRENTS
In class, get a 1.5V battery, 1 bulb and only 1 wire. Your challenge is to light the bulb. Draw here the right connection(s)
(source: Physics of everyday phenomena, Mac-Graw-Hill)
You just have built a simple electric circuit. An electric circuit is analogous to a water circuit.
A) The battery, like a water wheel
or water fall, give the charges POTENTIAL ENERGY. A water wheel gives
water GRAVITATIONAL potential energy but a battery gives charges
ELECTRIC potential energy. Each coulomb of charge (1C), coming out of
the positive pole has an energy of 1.5 J. (see figure). The battery has a potential (or voltage ) of 1.5V.
B) the charges flow through the wire carrying their potential energy like water flowing through pipes. THey flow trough the side of the bulb, through the filament and through the bottom of the bulb back to the battery. While passing through the filament the POTENTIAL ENERGY is converted to LIGHT ENERGY and THERMAL ENERGY.
In an incandescent lamp only 10% is used as light. The rest is lost to heat. Fluorescent bulb is much more efficient.
C) The charges have lost all their POTENTIAL energy they go through the battery again get another boost of 1.5 J per charge. The battery is analogous to a water pump. THe cycle starts again until there is no more energy in the battery.
D)
A
battery of potential 12V (voltage) gives each charge of 1C a potential
energy of 12J. WHile flowing in the circuit, the charges lose
their energy because some device will transform the potential
energy into another form of energy. All these devices have a resistance
noted R. THe energy lost per second
(Electric power) is proportional to R. In the same way, the water has a
potential energy because it is raised above ground level, the initial
energy is spent has it go through the pipes and encounter resistance.
source: http://www.windows.ucar.edu/tour/link=/spaceweather/how_circuit_works.html
end by an electric field and move a tiny bit in one direction. Since they all move a tiny bit in the same direction, the overall effect if a flow. (their velocity is called the drifting velocity)
B) If you cut a pipe, the water will spill. If you cut a circuit, the charges will stop flowing. An open switch don't hold charges the same way a faucet holds water. But it is a nice model, and I will use it:
So
every thing happens like the
battery gives each charge of 1C potential energy. The potential
energy is
converted to another form of energy. The conversion is never 100%
efficient. Some energy will converted to thermal energy. (A bulb gets
hot, the wires get hot, the battery gets hot ...). Once the charge have
no more energy, they flow through the battery (the pump here) and get a
new boost.
(source: Physics of everyday phenomena, Mac-Graw-Hill)
The bulb, the battery and the wire resist the flow of charges and take some of their energy. We say that they have resistance.
This is the way you should draw a simple circuit:
2)
Electricity provides the mean to transfer large quantities of energy great distance with little lost. Electric energy can be converted into other forms of energy:
A motor transforms electric energy to ____________ and thermal energy.
A bulb transforms .................................. to ------------------ and ----------------/
A speaker transforms _______________ to ___________ and ________________.
A radiator transforms ________________ to ______________.
A generator converts (tricky) __________ to ______________.and ____________. A generator produce electricity by spinning a magnet inside a coil (circuit). To make the wheel spins you can use a crank if it is a small generator.
3) If the potential of a battery is 9V, then each coulomb of charge (1C) carries ___________ J.
4) REmember, in a given circuit, the voltage or potential is the energy (PE energy) carried by a charge of 1C. (per coulomb of charge). So, when a charge of 1C has an electric of 1J, it has a potential of 1V. When a charge of 2C has an electric energy of 2J, its potential is ________ V. (potential (V)= energy(J)/charge (C) )
5) If a conductor connected to the terminal of a battery has a potential of 12 volts, then each coulomb of charge on the conductor has an energy of ______________.
6) If a charge of 1C has an energy of 5000J, its voltage is __________ V.
7) If a charge of 0.0001C has an energy of 0.5J , its voltage is _____________V.
8) Voltage is PE (potential energy ) per ___________
PART2: THe electric current and Electric Power
remember ? Power (watt) = Energy (J) supplied per second (for every second)
1) read:The electric current is noted I. The current is the number of charges of 1C that flow in a circuit in 1s.
Or I is the rate of flow of electric charge. The unit is the ampere (A).
I = 1 A, means that 1 coulomb of charge flows every second in a circuit. 1C/s = 1A. The ampere is named after a FRench scientists Andre Marie Ampere (1775-1836). An ammeter is a device that measures current.
2) Suppose you build a circuit made of a generator (V= 120V) and a motor. Suppose the current through a motor is 3A that is 3C/s. The potential of the generator is 120V.
THis means that each coulomb supplies the motor with ______J.
Per second, 3 coulombs flow in the motor. So the total amount of energy delivered by the generator in 1 second is therefore: ________ J/s = __________ watts.
(the energy delivered per second is the power delivered).
conclusion: the power rating of an electric device is found by multiplying the voltage V by the current I:
INDEX CARD
Voltage = Energy (J)/Charge (C)
Power (W)= Energy(J)/time(S) = voltage (V) x I (A)
I= current (A) = charge (C)/time (S)
3) A motor delivers 0.5A of current to an electric motor connected across its terminals .
voltage = 12V
A) What is the power rating of the motor (P = I x V)
B) How much energy does the motor use is 5 minutes ?
4) Answer these questions:
A) The units of electric potential difference are:
amperes ? volts? ohms? watts?
B) It is common to call electric potential difference (like 1.5V)
voltage? amperage? wattage?
C) The flow of electric charge is called electric
voltage ? current? power ?
and is measured in: ohms ? amperes? watts?
5) A current of 1 ampere is a flow of charge at the rate of ____ coulomb per second.
B) When a charge of 15C flows through any area in a circuit each second, the current is ______A.
c) When a lamp is plugged into a 120V socket, each coulomb of charge that flows in the current is raised to a potential energy of __________ J.
6) The current through a toaster connected to a 120V source is 8A. What is the power rating of the toaster ?
7) What current flows through a 75W light bulb connected to a 120V outlet?
8) The current through the starter motor of a car connected to a 120V battery is 210A. WHat electric energy is delivered to the starter in 10s? in 10 minutes? in 10 hours?
PART3: Ohm's law
lab electricity 1: introduction circuits, Ohm's law
1) Read and complete. Any conductor (bulb, battery, motor, generator, AC , the connecting wires) offers resistance to an electric current. The German Scientists Georg Simon Ohm found that the ratio between the potential difference V between the ends of the conductor and the current I is constant for many materials
This ratio is the resistance R of the material . So R = ____ / ______ or I = ____ / _____
So the current varies directly with the applied _____ and inversely with __________________.
The current I is in amperes (A) , the potential V is in volts (V) and the resistance is in ohms (Ω ).
The relationship says: for a potential of 1V, and a resistance of 1 Ω the current is 1A.
Some devices are called resistors. They are designed to have a designed resistance.
2) What is the current through a 30 Ω resistance that has a potential difference of 120 V?
3) AN automobile headlight with a resistance of 30Ω is placed across a 12V battery. What is the current through the circuit ?
4) A voltage of 75V is placed across a 15 Ω resistor what is the current through the resistor ?
5) A lamp draws a current of 0.5 A when it is connected to a 120V source.
A) what is the resistance of the lamp?
B) What is the power rating of the lamp ?
C) compute the expression RI2. conclusion?
6) A transistor uses 2 10-4 A of current when it is operated by a 3V battery. What is the resistance of the radio circuit?
7) Match each item in Column 1 with the most appropriate item in column2.
1. energy used a. represents one coulomb of charge flowing per second
2. KWh b. joule per second
3. watt c. unit of charge
4. kilowatt d. measured in volts
5. coulomb e. flow of electrical charges
6. current f. unit of measure in electric meters
7. ampere g. 1000 watts
8. potential difference h. power x time
8) A resistor was held at constant temperature in an operating electric circuit. A student measured the current thought the resistor and the potential difference across it. The measurements are shown in the data table below.
A) Using the information in the data table, construct a graph. (y = potential, x= current)
- Mark an appropriate scale on the axis labeled current (A).
- Plot the data points - give a title and label the axis - Draw the best fit line
B) Using your graph, find the slope of the best fit line. Use a ruler. Don't connect the points
hint: slope = rise/run = (y2-y1)/(x2-x1)
C) What physical quantity does the slope represent? What is the Unit ?
9) THe graph below represents the relationship between the potential difference across a metal conductor and the current through the conductor at constant temperature.
What is (approximately) the resistance of the conductor ?
hint: find the slope = rise/run or (y2-y1)/ (x2-x1) . The slope is the resistance of the circuit/
Part IV: Diagramming Electric Circuits
1)read and observe. Here are some electric circuit symbols:
source: http://www.pschweigerphysics.com/dccircuits.html
An Ammeter is used to measure the current flowing in a circuit.
The Voltmeter is used to measure the voltage of a device.
Here is an example. Suppose we have a battery of 30V connected to a resistance R of15 Ω
in a simple circuit. In our circuit we also include an ammeter to read
the current and a voltmeter to read the potential difference across the
resistance R.
Note that the voltmeter one terminal connected to one side of the element (resistor here) and the other one to the other side. This connection is called a parallel connection. The potential difference across the element is equal to the potential difference across the voltmeter.
Note that the ammeter measures the current. All the charges have to pass through it. It behaves like the main wire. Such a connection is called a series connection
2) Draw a schematic to show a circuit that includes a 90V battery, an ammeter, and a resistance of 45 Ω. What is the ammeter's reading ?
(that is find the current I)
3) Draw a circuit diagram to include a 60V battery, an ammeter, and a resistance of 12.5 Ω. Indicate the ammeter reading.
4) Draw a circuit diagram to include a 16 Ω resistor, a battery, and an ammeter that reads 1.75A. Indicate the voltage of the battery. Include also a voltmeter to read the voltage of the battery and another one to read the voltage of the resistor.
PART V more advanced - more on Ohm's law and drifting velocity
1) If you apply a voltage across a wire of copper, the electrons " feel" the electric field and try to move from - to +.
But encounter resistance in the circuit because they bump into the atoms of copper.
They end up drifting slightly toward the -. The velocity is called the drifting velocity.
Suppose at 300K (room temperature), the free electrons of the copper have a average speed of about = 106m/s
(thermal motion). The time between 2 collision is t = 3 10-14 sec.
The number of electrons per m3 is 1029.
THat's about 1 electron per atom.
A) the electric field applied is F = e E and E = V / d
and F = m a Compute the drifting speed. given t = 3 10-14 sec d= 10m and V = 10V and mass electron = 9.1 10-31kg
a = m/s/s
Then find the drifting speed s = a t = _____ m/s
B) At that speed how long it would take the electrons to drift over 10 meters ?
C) Let' s call A the area of a wire of copper, n the number of electron per volume, m the mass of an electron, e the charge of an electron,
t the time bet. ween collision and E the electric field the electrons feel inside the wire, I is the current or charge (C) flowing in 1 second.
Show that I = (e2 n t / m) A E
(hint: use acceleration = E e / m and speed = a t . REmember I = Q / t with t = 1 second Q = total of electrons flowing in the wire in 1 second)
D) (e2 n t / m) is called the resitivity σ . It depends on the properties of the substance (like copper) at a given temperature.
It is a measure of the material's ability to conduct electricity or electric current.
J = σ E where J is the current density.
Show that V = (d/ σ A) I where d is the length of the wire , A the area of the cross section, V the voltage.
if R = (d/ σ A) This is Ohms LAW : V = R I
ρ = 1/σ is called the resistivity so R = d/ σ A = d ρ /A
2) R = d/ σ A
consider a wire of area of 1mm x 1mm x 1mm and length 1 m
fill the table below. suppose V = 1V
3) The resistance depends on t the time between collision. Therefore R depends on the temperature.
as T increases, t decreases so R increases. What happens to Ohms law when the temperature changes ?
The relationship between the Voltage and the current is not linear anymore. The line curved down.
For the same voltage, the same resistance, the current is less because the resistance is more. As the voltage increases, the current increases,
the temperature rises limiting even more the rise of the current.
SAy the opposite phenomenon happens and you have a circuit with a light bulb. . As the temperature increases (light bulb getting
hotter and hotter), if the resistance goes down, the current would increase, the bulb would get even hotter ....then ....
what ?
4) experience to do.
Dry air has a high resitivity (4 1013). Charge an electroscope. The 2 strips can stay a part for a long time before the electroscope slowly discharges.
The air can be ionized (nitrogen and oxygen) if the air is heated. (see chapter about lightning) . The current is now due to the ions.
The conductivity can increase a lot. You can show this very simply. Use a charged electroscope and a candle.
On a hot dry air, the electroscope won't discharge but if you heat the air around (ionizing it) the strips move back together !
5) experience to do.
likewise distilled water has a large resistivity. However, if salt is added (sea) the conductivity can be multiplied by a factor
between 1000 to 1000,000 The ions are Cl- and Na +. If the resistivity of distilled water is 2 M Ω m
what is the resistivity of salty water ? (suppose the factor is 1000,000).
Experience to do:
Fill an aquarium with distilled water and place 2 flat electrondes of known areas. (find areas). Place the electrondes
at a given distance from each other. Find the resistance of the unit electrondes in water. (use resistivity, area, distance see 2) for formula ).
R = _________ Ω
Connect the electrodes in series with a 9V battery and a light bulb (3V) . is the light lighted up ? or the resistance too high ?
Now fill the aquarium with water + salt (3% of weight). Can you light the bulb ?
You can also move the electrodes closer to each other farther to see how the brightness changes as a function of the distance.
You can measure the current and build the relationship between the distance and the current,
6) Compute the resistance of your shoes. Suppose the height is 1cm (d = 0.01 in formula for R)
the area is 1 foot x 10 cm (find A but convert to meters first). Suppose the resistivity is 1010 Ω m
R = _______ Ω
7) The voltage of the Van Graff (the big one) is about 200,000 Volts. The resistance of your shoes is 2 109Ω
Find the current generated. I = ______ A convert to micro amps.
actually the Van Graaf can only hold a charge of 10 micro amps, so no more than 10 micro amps per second.
This is so small that the resistance of the shoes won't hold the charge. that's why you need to step
on a stool to be isolated from the ground. That's why if you touch an electroscope, the charge will leak very quickly.
If you remove the shoes they leak even faster.
You can charge an electroscope by rubbing your shoes against a carpet but you need to scuff constantly.
As soon as you stop, the charges leak away. It won't work of the day is wet. The water has more conductivity than air.
8) experimet to do
Build a battery with onions and strips of Zinc and copper
See you how the voltage increases with the number of onions.
You can also light a bulb with 4 big onions. With the light,
See how when you draw the current, the voltage of the power source (onions) decreases
because of the internal resistance .
Thanks Sadasia + .. Amber + CHris
In class, get a 1.5V battery, 1 bulb and only 1 wire. Your challenge is to light the bulb. Draw here the right connection(s)
(source: Physics of everyday phenomena, Mac-Graw-Hill)
You just have built a simple electric circuit. An electric circuit is analogous to a water circuit.
1) PLEASE READ
B) the charges flow through the wire carrying their potential energy like water flowing through pipes. THey flow trough the side of the bulb, through the filament and through the bottom of the bulb back to the battery. While passing through the filament the POTENTIAL ENERGY is converted to LIGHT ENERGY and THERMAL ENERGY.
In an incandescent lamp only 10% is used as light. The rest is lost to heat. Fluorescent bulb is much more efficient.
C) The charges have lost all their POTENTIAL energy they go through the battery again get another boost of 1.5 J per charge. The battery is analogous to a water pump. THe cycle starts again until there is no more energy in the battery.
D)
A
battery of potential 12V (voltage) gives each charge of 1C a potential
energy of 12J. WHile flowing in the circuit, the charges lose
their energy because some device will transform the potential
energy into another form of energy. All these devices have a resistance
noted R. THe energy lost per second
(Electric power) is proportional to R. In the same way, the water has a
potential energy because it is raised above ground level, the initial
energy is spent has it go through the pipes and encounter resistance. source: http://www.windows.ucar.edu/tour/link=/spaceweather/how_circuit_works.html
There is some limitation to this model:
A) To ease your understanding we will pretend that positive charges ,
each carrying 1C of charge, are flowing from + to -. EAch charge ,
carrying each 1C, has an energy of 12J (If the battery voltage is
12V). Actually, only electrons are flowing and they flow from -
to +. You need a large group of electrons of make 1C (1 electron = 1.6
E -19C). Also, electrons are not really flowing from one terminal to the other. They are pulled toward the +end by an electric field and move a tiny bit in one direction. Since they all move a tiny bit in the same direction, the overall effect if a flow. (their velocity is called the drifting velocity)
B) If you cut a pipe, the water will spill. If you cut a circuit, the charges will stop flowing. An open switch don't hold charges the same way a faucet holds water. But it is a nice model, and I will use it:
So
every thing happens like the
battery gives each charge of 1C potential energy. The potential
energy is
converted to another form of energy. The conversion is never 100%
efficient. Some energy will converted to thermal energy. (A bulb gets
hot, the wires get hot, the battery gets hot ...). Once the charge have
no more energy, they flow through the battery (the pump here) and get a
new boost.(source: Physics of everyday phenomena, Mac-Graw-Hill)
The bulb, the battery and the wire resist the flow of charges and take some of their energy. We say that they have resistance.
This is the way you should draw a simple circuit:
2)
Electricity provides the mean to transfer large quantities of energy great distance with little lost. Electric energy can be converted into other forms of energy:
A motor transforms electric energy to ____________ and thermal energy.
A bulb transforms .................................. to ------------------ and ----------------/
A speaker transforms _______________ to ___________ and ________________.
A radiator transforms ________________ to ______________.
A generator converts (tricky) __________ to ______________.and ____________. A generator produce electricity by spinning a magnet inside a coil (circuit). To make the wheel spins you can use a crank if it is a small generator.
3) If the potential of a battery is 9V, then each coulomb of charge (1C) carries ___________ J.
4) REmember, in a given circuit, the voltage or potential is the energy (PE energy) carried by a charge of 1C. (per coulomb of charge). So, when a charge of 1C has an electric of 1J, it has a potential of 1V. When a charge of 2C has an electric energy of 2J, its potential is ________ V. (potential (V)= energy(J)/charge (C) )
5) If a conductor connected to the terminal of a battery has a potential of 12 volts, then each coulomb of charge on the conductor has an energy of ______________.
6) If a charge of 1C has an energy of 5000J, its voltage is __________ V.
7) If a charge of 0.0001C has an energy of 0.5J , its voltage is _____________V.
8) Voltage is PE (potential energy ) per ___________
PART2: THe electric current and Electric Power
remember ? Power (watt) = Energy (J) supplied per second (for every second)
1) read:The electric current is noted I. The current is the number of charges of 1C that flow in a circuit in 1s.
Or I is the rate of flow of electric charge. The unit is the ampere (A).
I = 1 A, means that 1 coulomb of charge flows every second in a circuit. 1C/s = 1A. The ampere is named after a FRench scientists Andre Marie Ampere (1775-1836). An ammeter is a device that measures current.
2) Suppose you build a circuit made of a generator (V= 120V) and a motor. Suppose the current through a motor is 3A that is 3C/s. The potential of the generator is 120V.
THis means that each coulomb supplies the motor with ______J.
Per second, 3 coulombs flow in the motor. So the total amount of energy delivered by the generator in 1 second is therefore: ________ J/s = __________ watts.
(the energy delivered per second is the power delivered).
conclusion: the power rating of an electric device is found by multiplying the voltage V by the current I:
P = V x I
INDEX CARD
Voltage = Energy (J)/Charge (C)
Power (W)= Energy(J)/time(S) = voltage (V) x I (A)
I= current (A) = charge (C)/time (S)
3) A motor delivers 0.5A of current to an electric motor connected across its terminals .
voltage = 12V
A) What is the power rating of the motor (P = I x V)
B) How much energy does the motor use is 5 minutes ?
4) Answer these questions:
A) The units of electric potential difference are:
amperes ? volts? ohms? watts?
B) It is common to call electric potential difference (like 1.5V)
voltage? amperage? wattage?
C) The flow of electric charge is called electric
voltage ? current? power ?
and is measured in: ohms ? amperes? watts?
5) A current of 1 ampere is a flow of charge at the rate of ____ coulomb per second.
B) When a charge of 15C flows through any area in a circuit each second, the current is ______A.
c) When a lamp is plugged into a 120V socket, each coulomb of charge that flows in the current is raised to a potential energy of __________ J.
6) The current through a toaster connected to a 120V source is 8A. What is the power rating of the toaster ?
7) What current flows through a 75W light bulb connected to a 120V outlet?
8) The current through the starter motor of a car connected to a 120V battery is 210A. WHat electric energy is delivered to the starter in 10s? in 10 minutes? in 10 hours?
PART3: Ohm's law
lab electricity 1: introduction circuits, Ohm's law
1) Read and complete. Any conductor (bulb, battery, motor, generator, AC , the connecting wires) offers resistance to an electric current. The German Scientists Georg Simon Ohm found that the ratio between the potential difference V between the ends of the conductor and the current I is constant for many materials
This ratio is the resistance R of the material . So R = ____ / ______ or I = ____ / _____
So the current varies directly with the applied _____ and inversely with __________________.
The current I is in amperes (A) , the potential V is in volts (V) and the resistance is in ohms (Ω ).
The relationship says: for a potential of 1V, and a resistance of 1 Ω the current is 1A.
Some devices are called resistors. They are designed to have a designed resistance.
2) What is the current through a 30 Ω resistance that has a potential difference of 120 V?
3) AN automobile headlight with a resistance of 30Ω is placed across a 12V battery. What is the current through the circuit ?
4) A voltage of 75V is placed across a 15 Ω resistor what is the current through the resistor ?
5) A lamp draws a current of 0.5 A when it is connected to a 120V source.
A) what is the resistance of the lamp?
B) What is the power rating of the lamp ?
C) compute the expression RI2. conclusion?
6) A transistor uses 2 10-4 A of current when it is operated by a 3V battery. What is the resistance of the radio circuit?
7) Match each item in Column 1 with the most appropriate item in column2.
1. energy used a. represents one coulomb of charge flowing per second
2. KWh b. joule per second
3. watt c. unit of charge
4. kilowatt d. measured in volts
5. coulomb e. flow of electrical charges
6. current f. unit of measure in electric meters
7. ampere g. 1000 watts
8. potential difference h. power x time
8) A resistor was held at constant temperature in an operating electric circuit. A student measured the current thought the resistor and the potential difference across it. The measurements are shown in the data table below.
| Current (A) | Potential Difference (V) |
| 0.01 | 2.3 |
| 0.02 | 5.2 |
| 0.03 | 7.4 |
| 0.04 | 9.9 |
| 0.05 | 12.7 |
A) Using the information in the data table, construct a graph. (y = potential, x= current)
- Mark an appropriate scale on the axis labeled current (A).
- Plot the data points - give a title and label the axis - Draw the best fit line
B) Using your graph, find the slope of the best fit line. Use a ruler. Don't connect the points
hint: slope = rise/run = (y2-y1)/(x2-x1)
C) What physical quantity does the slope represent? What is the Unit ?
9) THe graph below represents the relationship between the potential difference across a metal conductor and the current through the conductor at constant temperature.
What is (approximately) the resistance of the conductor ?
hint: find the slope = rise/run or (y2-y1)/ (x2-x1) . The slope is the resistance of the circuit/
Part IV: Diagramming Electric Circuits
1)read and observe. Here are some electric circuit symbols:
source: http://www.pschweigerphysics.com/dccircuits.htmlAn Ammeter is used to measure the current flowing in a circuit.
The Voltmeter is used to measure the voltage of a device.
Here is an example. Suppose we have a battery of 30V connected to a resistance R of15 Ω
in a simple circuit. In our circuit we also include an ammeter to read
the current and a voltmeter to read the potential difference across the
resistance R. Note that the voltmeter one terminal connected to one side of the element (resistor here) and the other one to the other side. This connection is called a parallel connection. The potential difference across the element is equal to the potential difference across the voltmeter.
Note that the ammeter measures the current. All the charges have to pass through it. It behaves like the main wire. Such a connection is called a series connection
2) Draw a schematic to show a circuit that includes a 90V battery, an ammeter, and a resistance of 45 Ω. What is the ammeter's reading ?
(that is find the current I)
3) Draw a circuit diagram to include a 60V battery, an ammeter, and a resistance of 12.5 Ω. Indicate the ammeter reading.
4) Draw a circuit diagram to include a 16 Ω resistor, a battery, and an ammeter that reads 1.75A. Indicate the voltage of the battery. Include also a voltmeter to read the voltage of the battery and another one to read the voltage of the resistor.
PART V more advanced - more on Ohm's law and drifting velocity
1) If you apply a voltage across a wire of copper, the electrons " feel" the electric field and try to move from - to +.
But encounter resistance in the circuit because they bump into the atoms of copper.
They end up drifting slightly toward the -. The velocity is called the drifting velocity.
Suppose at 300K (room temperature), the free electrons of the copper have a average speed of about = 106m/s
(thermal motion). The time between 2 collision is t = 3 10-14 sec.
The number of electrons per m3 is 1029.
THat's about 1 electron per atom.
A) the electric field applied is F = e E and E = V / d
and F = m a Compute the drifting speed. given t = 3 10-14 sec d= 10m and V = 10V and mass electron = 9.1 10-31kg
a = m/s/s
Then find the drifting speed s = a t = _____ m/s
B) At that speed how long it would take the electrons to drift over 10 meters ?
C) Let' s call A the area of a wire of copper, n the number of electron per volume, m the mass of an electron, e the charge of an electron,
t the time bet. ween collision and E the electric field the electrons feel inside the wire, I is the current or charge (C) flowing in 1 second.
Show that I = (e2 n t / m) A E
(hint: use acceleration = E e / m and speed = a t . REmember I = Q / t with t = 1 second Q = total of electrons flowing in the wire in 1 second)
D) (e2 n t / m) is called the resitivity σ . It depends on the properties of the substance (like copper) at a given temperature.
It is a measure of the material's ability to conduct electricity or electric current.
J = σ E where J is the current density.
Show that V = (d/ σ A) I where d is the length of the wire , A the area of the cross section, V the voltage.
if R = (d/ σ A) This is Ohms LAW : V = R I
ρ = 1/σ is called the resistivity so R = d/ σ A = d ρ /A
2) R = d/ σ A
consider a wire of area of 1mm x 1mm x 1mm and length 1 m
fill the table below. suppose V = 1V
| σ | ρ | R | I | |
| good conductor, Au , Ag, Cu | 108 | |||
| good insulator | 10-12 | |||
| glass , quartz | 10-16 |
3) The resistance depends on t the time between collision. Therefore R depends on the temperature.
as T increases, t decreases so R increases. What happens to Ohms law when the temperature changes ?
The relationship between the Voltage and the current is not linear anymore. The line curved down.
For the same voltage, the same resistance, the current is less because the resistance is more. As the voltage increases, the current increases,
the temperature rises limiting even more the rise of the current.
SAy the opposite phenomenon happens and you have a circuit with a light bulb. . As the temperature increases (light bulb getting
hotter and hotter), if the resistance goes down, the current would increase, the bulb would get even hotter ....then ....
what ?
4) experience to do.
Dry air has a high resitivity (4 1013). Charge an electroscope. The 2 strips can stay a part for a long time before the electroscope slowly discharges.
The air can be ionized (nitrogen and oxygen) if the air is heated. (see chapter about lightning) . The current is now due to the ions.
The conductivity can increase a lot. You can show this very simply. Use a charged electroscope and a candle.
On a hot dry air, the electroscope won't discharge but if you heat the air around (ionizing it) the strips move back together !
5) experience to do.
likewise distilled water has a large resistivity. However, if salt is added (sea) the conductivity can be multiplied by a factor
between 1000 to 1000,000 The ions are Cl- and Na +. If the resistivity of distilled water is 2 M Ω m
what is the resistivity of salty water ? (suppose the factor is 1000,000).
Experience to do:
Fill an aquarium with distilled water and place 2 flat electrondes of known areas. (find areas). Place the electrondes
at a given distance from each other. Find the resistance of the unit electrondes in water. (use resistivity, area, distance see 2) for formula ).
R = _________ Ω
Connect the electrodes in series with a 9V battery and a light bulb (3V) . is the light lighted up ? or the resistance too high ?
Now fill the aquarium with water + salt (3% of weight). Can you light the bulb ?
You can also move the electrodes closer to each other farther to see how the brightness changes as a function of the distance.
You can measure the current and build the relationship between the distance and the current,
6) Compute the resistance of your shoes. Suppose the height is 1cm (d = 0.01 in formula for R)
the area is 1 foot x 10 cm (find A but convert to meters first). Suppose the resistivity is 1010 Ω m
R = _______ Ω
7) The voltage of the Van Graff (the big one) is about 200,000 Volts. The resistance of your shoes is 2 109Ω
Find the current generated. I = ______ A convert to micro amps.
actually the Van Graaf can only hold a charge of 10 micro amps, so no more than 10 micro amps per second.
This is so small that the resistance of the shoes won't hold the charge. that's why you need to step
on a stool to be isolated from the ground. That's why if you touch an electroscope, the charge will leak very quickly.
If you remove the shoes they leak even faster.
You can charge an electroscope by rubbing your shoes against a carpet but you need to scuff constantly.
As soon as you stop, the charges leak away. It won't work of the day is wet. The water has more conductivity than air.
8) experimet to do
Build a battery with onions and strips of Zinc and copper
See you how the voltage increases with the number of onions.
You can also light a bulb with 4 big onions. With the light,
See how when you draw the current, the voltage of the power source (onions) decreases
because of the internal resistance .
Thanks Sadasia + .. Amber + CHris