Physics and chemistry
Unit 7: Electricity and magnetism
Unit 7. Electricity and magnetism
Index
1.-Electrification:...............................................................................................................2
2- Coulomb’s law...............................................................................................................3
3. Electric field vs Magnetic field.....................................................................................5
Types of magnets:...................................................................................... 6
Some uses of magnets:.............................................................................. 7
4. Electric circuits..............................................................................................................7
Basic Properties of Electric Circuits............................................................8
5. Ohms Law......................................................................................................................9
Ohms Law Relationship..........................................................................9
6. Connecting resistors....................................................................................................10
6.1 Resistors in series............................................................................... 10
Current................................................................................................. 10
6.2 Resistors in parallel............................................................................ 12
6.3 Mixed circuits..................................................................................... 13
7. Power...........................................................................................................................14
Practice exam...................................................................................................................15
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Physics and chemistry
Unit 7: Electricity and magnetism
1.-Electrification:
It is the phenomenon whereby objects acquire an electric charge.
The number of protons in an atom equals the number of electrons; therefore atoms are
neutral. However, atoms may gain or lose electrons, thereby getting an electric charge.
An object is charged positively if the atom has lost electrons.
An object is charged negatively if the atom has gained electrons.
How is electric charge measured? Coulombs (C).
Remember:
1 e- has a charge of 1.6·10-19 C
Other submultiples used:
1 mC = 10-3 C
1 μC
-6
= 10 C
(milicoulomb)
(microcoulomb)
1 nc = 10-9 C
(nanocoulomb)
1 pc = 10-12 C
(picocoulomb)
1.1 Methods of electrification:
-
By friction.
-
By induction.
-
By contact.
1.2 Conducting and insulating materials.
-
Conductors: they allow the electric charges to move freely through them, e.g.
copper.
-
Insulators: they do not allow free flow of charges inside them. e.g wood
Activities:
1.- When an object loses e-, how is its charge?
2.- Say by which methods are objects electrified in the following experiences:
a) We rub a glass rod with a silk scarf.
b) We approach an electrified glass rod to a neutral ball.
c) We touch a neutral ball with an electrified rod.
d) You comb your dry hair with a plastic comb.
e) You now approach the comb to a trickle of water running from the tap.
3.- Cables of electric supply are lined with plastic. Why?
4.- When rubbing a plastic sheet with a woolen garment, the sheet acquires a 0. 5 pC
charge. How many e- in excess does the sheet have?
Sol: 3.125 . 106
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Unit 7: Electricity and magnetism
5.- How many electrons lacks an object with a charge of +2.5 nC?
Sol: 1.56 . 1010
6.- How many e- has in excess an object with a charge of -3 μC?
Sol: 1.875 . 1013
7.- What charge has an object that has 2·106 electrons in excess?
Sol: 3.2 . 10-13 C
8.- What charge has an object that has 1.3 . 108 electrons below?
Sol: 2.08 . 10-11 C
2- Coulomb’s law
It was discovered by Priestley in 1766, and rediscovered by Cavendish few years later,
but it was Coulomb in 1785 who submitted it to experimental testing.
Coulomb’s law states that “the magnitude of the Electrostatics force of interaction
between two point charges is directly proportional to the product of their charges
and inversely proportional to the square of the distances between them, and has
the direction of the line connecting them. The force is repulsive if the charges have
the same sign, and attractive if they have different sign.”
Concerning Coulomb’s law it is important to state the following:
1- Point charge means an electric charge located on a geometrical point in space.
Obviously, such point charge does not really exist, it is an idealized concept, but
it serves as a good approach when we study interaction between electrically
charged bodies whose dimensions are very small compared with the distance
between them.
2- When we speak of the force between electric charges we always assume that
they are at rest (hence the term Electrostatics);
It is to be noted that electrical force is a vector quantity- it has magnitude, direction
and sense.
In mathematical terms, this law refers to magnitude F of the force which each of the two
point charges q1 and q2 exert on each other separated by a distance r and is expressed as
an equation as:
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Unit 7: Electricity and magnetism
K being a constant known as Coulomb’s constant and the bars meaning absolute value
(we work without a sign). The value of K in vacuum is 9·109 N·m2/C2
Units:
Force is expressed in Newtons (N).
Charges in coulombs (C)
Distance in meters.(m)
F is the force vector for the electric charges. It can be attractive or repulsive, depending
on the sign that appears (signaling whether the charges are positive or negative).
Activities:
9- Two electrically charged particles are placed at a distance of 4 mm between them; the
magnitude of the electric charges being q1= 6 μC and q2 = -12,0 μC. What is the
magnitude of the electrical force exerted on each electric charge? Draw a scheme with
the forces.
Sol: a) 4·104 N
10- Determine the force acting on the following electric charges q1= +1· 10-6 C and
q2= +2· 10-5 C. Which are at rest and in vacuum at a distance of 5 cm. Will it be
attractive or repulsive? Draw a scheme with the forces.
Sol: 72 N
11- Determine the distance between two charges, q1= -1,25· 10-9 C. and q2= +2· 10-5 C.
Which are at rest and in vacuum if they attract each other with a force of 2.25·10-2N.
Sol: 0.1 m
12- Two equal electric charges located at a distance of 2 m repel one another in vacuum
with a force of 9·10-3 N. Calculate the value of the electric charges.
Sol: 2 μC
13- A charge of +12 μC attracts another charge with a force of 0.25 N when they are in
vacuum at 20 cm of distance. What is the value of the other charge? What is its sign?
-8
Sol: 9·10 C; negative
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Physics and chemistry
Unit 7: Electricity and magnetism
-3
14- A charge of +850 nC repels another charge of +425 nC with a force of 3.8· 10 N.
Calculate the distance between them assuming they are both in vacuum.
Sol. 0.92 m
15- Calculate the force with which two charges of 5mC and -3mC attract each other if
they are in vacuum at a distance of 2 m.
Sol: 3.375·104 N
16- Work out the value of two equal charges if we know they repel each other with a
force of 10-5 N when they are at a distance of 3m.
Sol: 10-7 C
17- How far must we place two charges of + 50 μC and -125 μC so that they attract
each other with a force of 1N?
Sol. 7.5 m
18- Two equal charges repel each other with a force of 10 N when they are placed at a
distance of 1cm. Calculate the value of these charges.
Sol: 3.3·10-10 C
3. Electric field vs Magnetic field.
Electric charge in bodies alters the space surrounding them. The charge creates an
electric field.
These are the lines that represent the electric field.
But exists another type of field, magnetic field that is created by a magnet.
A magnet is an object made of certain materials which creates a magnetic field. Every
magnet has at least one north pole and one south pole. By convention, we say that the
magnetic field lines leave the North end of a magnet and enter the South end of a
magnet.
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Unit 7: Electricity and magnetism
This is an example of a magnetic dipole ("di" means two, thus two poles). If you take a
bar magnet and break it into two pieces, each piece will again have a North pole and a
South pole. If you take one of those pieces and break it into two, each of the smaller
pieces will have a North pole and a South pole. No matter how small the pieces of the
magnet become, each piece will have a North pole and a South pole. It has not been
shown to be possible to end up with a single North pole or a single South pole which is
a monopole ("mono" means one or single, thus one pole)
By the end of the 18th century, scientists had noticed many electrical phenomena and
many magnetic phenomena, but most believed that these were distinct forces. Then in
July 1820, Danish natural philosopher Hans Christian Oersted published a pamphlet that
showed clearly that they were in fact closely related.
During a lecture demonstration, on April 21, 1820, while setting up his apparatus,
Oersted noticed that when he turned on an electric current by connecting the wire to
both ends of the battery, a compass needle held nearby deflected away from magnetic
north, where it normally pointed.
This was the one and only conclusion:
So charge in motion creates magnetism
Magnets but also electric current creates magnetic field.
Types of magnets:
1. A permanent magnet is an object made from a material that is magnetized and
creates its own persistent magnetic field. An everyday example is a refrigerator magnet
used to hold notes on a refrigerator door. Materials that can be magnetized, which are
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Unit 7: Electricity and magnetism
also the ones that are strongly attracted to a magnet, are called ferromagnetic. These
include iron, nickel, cobalt.
2. An electromagnet is made from a coil of wire that acts as a magnet when an electric
current passes through it but stops being a magnet when the current stops.
So electric charges in motion create magnetic field. Is it possible the opposite?
When Michael Faraday made his discovery of electromagnetic induction in 1831, he
hypothesized that a changing magnetic field is necessary to induce a current in a nearby
circuit. To test his hypothesis he made a coil by wrapping a paper cylinder with wire. He
connected the coil to a galvanometer, and then moved a magnet back and forth inside
the cylinder.
This was the one and only conclusion:
So a magnet in motion creates electric current
Some uses of magnets:
1. They are used to construct the electrical motors and the generators which convert
the electrical energy into mechanical energy and vice verse.
2. They are also used in the speakers which can convert the electrical energy into
sound energy.
3. They are used in the electrical bells.
4. They are used in the Maglev trains. In the Maglev trains, the super conducting
magnets are used on the tracks on which the train floats. These types of the trains
are working on the repulsion force of the magnets.
5. They are also used to sort out the magnetic and non magnetic substances from
the scrap(chatarra)
6. They are used in TV screens, computer screens, telephones and in tape recorders.
7. They are used in the refrigerators to keep the door close.
8. The compass which is used to find the geographical directions.
4. Electric circuits
Magnitudes in electric circuits:
1. Charge (unit: coulomb, C; letter symbol: q or Q )
The electric charge is the most basic quantity in electrical engineering, and arises from
the atomic particles of which matter is made.
2. Potential Difference (unit: volt, V; letter symbol: V )
The potential difference, also known as voltage , is the energy required to
move a unit positive charge from one point to another across a circuit element.
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3. Current (unit: ampere, A; letter symbol: I)
The electric current is the rate of charge flow in a circuit. I = Q/t
4. Power (unit: watt , W; letter symbol: P )
The electric power is the rate of change of energy. P = W/tCircuits are collections of
circuit elements and wires. Wires are designated on a schematic as being straight lines.
An electronic circuit is composed of individual electronic components, such as
resistors, connected by conductive wires through which electric current can flow. So it
is necessary a source of energy like batteries.
Basic Properties of Electric Circuits
• A circuit is always a closed path.
• A circuit always contain an energy source which acts as source of electrons.
• In an electric circuit flow of electrons takes place from negative terminal to
positive terminal.
• Direction of flow of conventional current is from positive to negative terminal.
An electrical circuit is an interconnection of electrical circuit elements. These
circuit elements can be categorized into two types, namely active elements and
passive elements.
Passive Circuit Elements
The most basic of the passive circuit elements is the resistance.
They consume energy (i.e. convert from electrical form to a non-electrical form such as
heat or light).
Resistance (unit: ohm, Ω; letter symbol: R )
The common circuit symbols for the Resistor are shown in figure 1. First figure is the
common symbol used for the general resistor, especially when hand-written. Second
figure is the most general symbol for the resistor, especially when in printed form.
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Unit 7: Electricity and magnetism
5. Ohms Law
The relationship between Voltage, Current and Resistance in any electrical circuit was
firstly discovered by the German physicist Georg Ohm. Ohm found that, at a constant
temperature, the electrical current flowing through a fixed linear resistance is directly
proportional to the voltage applied across it, and also inversely proportional to the
resistance. This relationship between the Voltage, Current and Resistance forms the
basis of Ohms Law and is shown below.
Ohms Law Relationship
V= I·R
V = Voltage (volts) (V)
I = Current (amperes) (A)
R = Resistance (ohms) (Ω)
By knowing any two values of the Voltage, Current or Resistance quantities we can use
Ohms Law to find the third missing value. Ohms Law is used extensively in
electronics formulas and calculations so it is “very important to understand and
accurately remember these formulas”.
To find the Voltage, (V)
[V=I·R]
To find the Current, (I)
I = V/R
To find the Resistance, (R)
R = V/I
Activities:
19. What is the value of this resistor, in ohms (Ω)?
sol: 2700 Ω
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20. An automobile headlight has an average resistance of 24 ohms. Car batteries provide
a potential difference of 12 volts. What amount of current passes through the headlight?
Sol: 0.5 A
21. An electric heater draws 3.5 A from a 110 V source. What is the resistance of the
heating element ?
Sol: 31.4 Ω
22. If 750 µA is flowing through 11 kΩ of resistance, what is the voltage drop across
the resistor?
Sol. 8.25 V
23. A resistance of 10 Ω is placed across a 9 V battery. What current flows through the
battery?
Sol. I = 0.9 A
6. Connecting resistors
6.1 Resistors in series
Current
I = I1 = I2=I3...etc
Resistance
Voltage
V = V1+V2+V3...etc
24. A series circuit has 4 resistances of 20, 40, 10 and 5 Ohms. Calculate the Total
resistance and the current flowing through each one if the battery has a value of 10 Volts
Solutions: Total resistance = 75 Ω. I = 0,13 A
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25. In this circuit, calculate:
a ) The total resistance in the circuit
b) The current flowing in the circuit.
c) The voltage across every resistor
Solutions:a) = 40 Ω b) = 0,225 A c ) V1 = 2,25 V2 =1,125 V3 = 5,625
26. In the circuit on the left, we have 3 series resistors. We measure 8 volts in the
voltmeter ( represented by V ).
a) Calculate the voltage across the 20 Ω resistance
b) Calculate the equivalent resistor and the current in the battery.
sol: V = 32 V; 35 Ω V = 56 V
27. In this circuit, the value of the battery is 1.5 Volts and the current measured in the
ammeter is 0.25A.
a) Calculate the value of Resistor 2 in this circuit.
b) How much current would flow if the value of R was doubled?
Solutions: R = 5 Ω and b) I = 0.136 A
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6.2 Resistors in parallel
Resistance
Voltage
Current
I = I1+I2+I3...etc
28- 5 ,10 and 25 Ohms resistors are connected in parallel. The value of the battery is 9
Volts Calculate the total resistance and the current flowing through each one
Solutions: Rt = 2,94 Ω I1 = 1,8 A I2= 0,9 A and I3 = 0,36 A
29. What will be the value of the current flowing through the 100 Ohm resistor?
And what about the current in the other resistor?
Calculate the total resistance of the circuit.
Solutions: I1 = 0,05 A and I2 = 0,1 A Rt = 33,33 Ω
30. The value of the battery is 12 Volts and the current in the battery 2.1 A. If R1 = 20 Ω
and R2 = 40 Ω . What is the value of R3 ?
Sol. 80 Ω
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Unit 7: Electricity and magnetism
6.3 Mixed circuits
31. Calculate the equivalent resistor and the current in the battery.
Sol: Solution: Re = 20 Ω I = 250 mA
32. Calculate the equivalent resistor and the current in the battery.
Re =64,18 Ω I = 77,9mA
33. In the next circuit , calculate the voltage across the 20 Ohm resistor.
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Unit 7: Electricity and magnetism
Solution: 1,64 volts
7. Power
Power is the measure of how much work can be done in a given amount of time.
• Mechanical power is commonly measured (in America) in “horsepower.”
• Electrical power is almost always measured in “watts,” and it can be calculated
by the formula P = I·V
• Electrical power is a product of both voltage and current, not either one
separately.
• Horsepower and watts are merely two different units for describing the same
kind of physical measurement, with 1 horsepower equaling 745.7 watts.
Activities:
34. There are 2 A of current in a circuit that has one 1.5 V battery. What is the electric
power consumed by the circuit?
Sol: 3W
35. The electric power consumed by a circuit with one light bulb is 3 W. The voltage of
the battery is 3 V. What is the current in the circuit?
Sol: 1A
36. Determine the amount of electrical energy (in J) used by the following devices when
operated for the indicated times.
a. Hair dryer (1500 W) - operated for 5 minutes
b. Electric space heater (950 W) - operated for 4 hours
c. X-Box video game player (180 W) - operated for 2 hours
d. 42-inch LCD television (210 W) - operated for 3 hours
sol: a. 4.5x105 J b. 1.4x107 J c. 1.3x106 J d. 2.3x106 J
37. A hair dryer has a resistance of 100 Ω and it is plugged to a 220 V. If it is operating
for 40 minutes, calculate how many kilowatts per hour of energy does it use and how
much do you pay if 1kwh = 0,20€.
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Unit 7: Electricity and magnetism
Practice exam
1. When is a substance positively charged? If a substance has a charge of -2 nC,
how many electrons has it gained? If a substance loses 3·1015 e-, how much
charge does it have? The electron’s charge is 1.6·10-19 C
Sol. 1.25·1010 e ,+4.8 ·10-4 C
2. Two charges, the first being +6 μC and the second, -2 μC, are 5 mm apart in
vacuum. What is the value of the force between them? Is it repulsive or
attractive? Make a graph of the charges and the forces between them.
K = 9·109 N·m2/C2
Sol.4320 N
3. Over the course of an 8 hour day, 3.8x104 C of charge pass through a typical
computer (presuming it is in use the entire time). Determine the current for
such a computer.
Sol. 1.3 A
4. Defibrillator machines are used to deliver an electric shock to the human
heart in order to resuscitate an otherwise non-beating heart. It is estimated
that a current as low as 17 mA through the heart is required to resuscitate.
Using 100,000 Ω as the overall resistance, determine the output voltage
required of a defibrillating device.
Sol. 1700 V
5. Two resistors with resistance values of 6.0 Ω and 8.0 Ω are connected to a
12.0-volt source. Determine the overall current in the circuit if the resistors
are
a. … connected in series.
b. … connected in parallel.
6. Complete:
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Physics and chemistry
Unit 7: Electricity and magnetism
sol.
7. A 541-Watt toaster is connected to a 120-V household outlet. What is the
resistance (in ohms) of the toaster?
Answer: R = 26.6 Ω
8. Fill the gaps.
a) Bar magnets have two poles:
and
pole.
b) The pushing or pulling force of a magnet is strongest
the magnet.
of
c)Like poles __________ each other while unlike poles ___________ each
other.
d) Some metallic materials are magnetic and some are not. An example of
magnetic is
and an example of non magnetic is
e) The three methods of electrification are:
f) Two charges with
sign attract each other.
g) The unit of charge in the SI is
h) Coulomb’s constant K depends on
i) An electrical conductor is
An example is
j) An electromagnet is
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with the letter