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WEEK 19
MAGNETISM AND
ELECTRICITY
ELECTRIC CIRCUITS.
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Resistance:
After this lesson, you should be able to do the following:
Know how to define resistance.
Know what resistance is.
Know the unit for resistance.
Know the properties of resistors connected in series.
Know the properties of resistors connected in parallel.
Know how to calculate the total resistance in a circuit.
1.
Resistance:
As you know by now, current is the flow of charge caused by a potential difference
across the ends of a conductor. A conductor is a substance that allows current to flow
through it. Some substances do not allow current to flow through them and they are
called insulators.
As you also know by now, all substances are made up of particles called atoms. These
atoms are in constant motion. As a result of this motion of the atoms, the electrons
flowing through the conductor collide with these moving atoms. These collisions hinder
the electrons to flow through the conductor and this prevention of the smooth flow of
charge is called resistance.
Resistance can therefore be defined as: the resistance of a conductor to the flow of
charge.
Resistance can be influenced by the following factors:
a)
The type of material that the conductor consists of. For example: Copper wire
lets a higher current through than Nichrome wire with the same thickness. This
means that the resistance of copper is less than that of nichrome.
b)
The length of the conductor. The longer the conductor the higher the resistance of
the conductor and the smaller the current that will flow through the conductor.
c)
The thickness of the conductor. The thicker the conductor the smaller the
resistance and the larger the current that will flow through the conductor.
d)
The temperature of the conductor. The hotter the conductor the higher the
resistance and the smaller the current that will flow through the conductor. If the
temperature of a conductor increases the atoms will move faster and more
collisions will occur with the flowing charge. This will hinder the charge to flow
much more than when the atoms do not move as fast.
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A conductor with a high resistance is called a resistor.
Resistance can be measure with a multimeter. A multimeter is an instrument that
measures electric current, potential difference and resistance.
So, to measure the
resistance with the multimeter, the switch on the multimeter must be switched to the
resistance function and the current must be switched off or the resistor must be removed
from the circuit.
2.
The unit of resistance:
The resistance of a resistor is measured in Ohm (Ω). This is named after a German
scientist George Ohm who lived from 1787 to 1854 and was called the father of electrical
circuit analysis.
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Ohm did a lot of experiments and he was able to define the relationship between voltage,
current and resistance. Unfortunately, when Ohm published his findings in 1827, his
ideas was dismissed by his colleagues and Ohm was forced to resign from his highschool position and he lived in poverty and shame until he accepted a position in
Nuremberg.
3.
The relationship between potential difference, current and resistance:
If we increase the number of cells in a circuit, we know that the potential difference as
well as the current increase. If we draw a graph of the potential difference against the
current, we see that the graph forms a straight line.
Resistor
V
I
The gradient of the graph is:
=R
We can use the gradient between any two points on the graph and we will get the same
answer. This answer will then be the resistance of the resistor.
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The abbreviation for resistance is R and we already know that the unit for resistance is
the ohm and that we use the Greek symbol Ω (omega) for ohm.
So, Resistance =
or as an equation: R =
The above formula is used to define the ohm:
A conductor has a resistance of one ohm if a current of one ampère passes trough it when
a potential difference of one volt is maintained across the ends of the conductor.
Example:
Calculate the resistance of a resistor if a current of 2 A flows through it and the potential
difference across the ends of the resistor is 6 V.
R=
=
= 3Ω
4.
Resistors connected in series:
Resistors connected in series means there is only one path for the current to flow. This
also means that the more resistors are connected in series, the more the restriction to the
flow of the current.
Let us consider the resistances as toll gates.
A
B
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In figure A we have only one toll gate (resistor) and all the cars will move through the
one toll gate.
In figure B we have three consecutive toll gates (resistors connected in series). All the
cars must move through all three toll gates causing a longer time lapse at the toll gates.
So the restriction to the flow of the traffic is much more than when we only have one toll
gate.
The same happens when we have resistors in series. The more resistors in series the
more the resistance of the circuit and the more the restriction to the flow of the current.
To determine the total resistance in a series circuit, we add the resistances.
RT = R1 + R2 + R3
According to the above circuit, the total resistance in the circuit will be:
RT = R1 + R2 + R3
= 1+2+3
= 6Ω
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The moment more resistors are added to the circuit, the total resistance increases.
RT = R1 + R2 + R3 + R4
= 1+2+3+4
= 10 Ω
We also know by now that the current in a series circuit is the same every where. There
is only one path for the current to flow.
However, the more resistors connected in series in the circuit, the smaller the current in
the circuit will become. This is because the emf of the battery remains constant.
Let us look at the following circuits and use the equation to determine the current flowing
through the circuit.
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The emf of the cell is 12 V and the total resistance in the circuit is 6 Ω. Let us calculate
the current flowing through the circuit.
R=
6 =
I =
= 2 A.
Let us take the same circuit and just add another resistor in series.
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The current through the circuit changes to the following:
R=
10 =
I =
= 1,2 A.
The current flowing through each resistor will therefore change from 2 A to 1,2 A.
As we have seen in the previous lesson, a series circuit is also a potential difference
divider. Let us just look at it again.
If we add another resistor in series, the voltmeter readings will change to the following:
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If you add all the potential differences, the total will still be 12 V.
5.
Resistors connected in parallel:
Each resistor in a parallel circuit provides a route for the current to flow through. The
more resistors in parallel, the more routes there are for the current to flow through.
Let us consider the example of the toll gates again.
Here we have three toll gates next to each other. This means that the oncoming traffic
can choose through which toll gate they want to go. It means that the time laps for the
traffic to move through the toll gates is much less than for the toll gates in series. So, the
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more toll gates there are, the less time it will take for the vehicles to move past. So, the
more resistors in parallel, the less resistance in the circuit.
The smaller the resistor, the bigger part of the current flows through that resistor.
The equivalent resistor for all the parallel resistors will be smaller than the smallest
resistor connected in parallel. The equivalent resistor means it is the single resistor that
we can use in the place of the parallel resistors which will have the same effect as all the
resistors connected in parallel.
We use the following equation to calculate the equivalent resistance for a parallel
connection:
=
+
+
However, if you only have two resistors connected in parallel, you can use the following
equation:
RP =
Let us have a look at some examples:
1.
What is the equivalent resistance in the following circuit?
As we have only two resistors in parallel, we can use the second equation.
RP =
=
= 1,2 Ω
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As you can see, the equivalent resistance is less than the smallest resistance namely 2 Ω
2.
What is the equivalent resistance in the following circuit.
In this case we can not use the second equation to determine the equivalent resistance.
We have to use the first equation because we have more than one resistor in parallel.
=
=
+
+
+
+
Now you have to determine the LCM which is 12
=
=
This is the answer for
and we want the answer for RP You
have to change both the fractions around.
RP =
= 0,92 Ω
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As you can see from the two examples above, the more resistors we connect in parallel,
the smaller the equivalent resistance become.
You know from the previous lesson that in a parallel circuit, the potential difference of
each resistor connected in parallel is the same as well as the same as the potential
difference across the whole parallel connection.
We also know that in the above case we have two paths for the current to pass through
and that the current will divide between the two paths. The current will not necessarily
divide in half. The division of the current depends on the resistance of the resistor. The
biggest part of the current will move through the smallest resistor but the sum of the
current through the branches of the parallel connection will be the total current in the
circuit.
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Example:
a)
Determine the equivalent resistance in the parallel connection.
As there are only two resistors in parallel, we use the equation for two resistors.
RP =
=
= 2Ω
b)
Calculate the total current in the circuit.
Here we use the formula because we have the emf as well as the equivalent
resistance.
R=
2 =
I =
= 1,5 A.
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c)
What is the magnitude of the current through R2?
The potential difference across the parallel connection is 3 V. We know by now
that the potential difference across R2 must also be 3 V.
R=
6 =
I =
= 0,5 A.
d)
What is the magnitude of the current through R1?
We know that the total current in the circuit is 1,5 A. If the current through R 2 is
0,5 A, the current through R1 must be 1 A.
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