resistance in electrical systems chap 4.3. objectives explain the difference between conductors,...
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Resistance in Electrical Systems
Chap 4.3
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Objectives
• Explain the difference between conductors, insulators & semiconductors.
• Define electrical resistance.• Solve problems using resistance, voltage &
current.• Describe a material that obeys Ohm’s law.• Calculate the resistance of a wire.• Solve circuit problems.
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Conductors
• Metals, some liquids and plasma have many free electrons than move freely in the presence of an electric field or potential difference
• Electric current can move easily in these materials. However, there is always some resistance to current flow.
• In some materials, resistance disappears at very low temperatures. These are called superconductors.
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Insulators
• Materials with tightly bound electrons do not conduct electric current well.
• These include most non-metallic solids such as wood, glass, rubber, etc.
• However, with a large enough potential difference, even an insulator will conduct a current. Lightning will travel through air, trees, soil and even concrete. People on sailboats with wooden masts have been electrocuted when the masts came in contact with overhead power lines.
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Semiconductors
• A semiconductor is a material which has electrical conductivity between that of a conductor and an insulator.
• The conductivity of a semiconductor increases with increasing temperature, behavior opposite to that of a metal.
• Semiconductors can display a range of useful properties such as passing current more easily in one direction than the other.
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Electrical resistance
• Electrons moving through a conductor do not travel in a straight line. They collide with the atoms of the conductor as well as with other electrons.
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Electrical Resistance – con’t
• The result of these collisions is that current flow is impeded or resisted.
• Electrical resistance is the ratio of the voltage drop across a device to the current flowing through it.
• R = V / I.• The unit of resistance is the ohm ( ).W• Thus a device has a resistance of 1 ohm when a
potential difference of 1 volt causes 1 amp of current to flow through it.
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Ohm’s lawIn 1826, German physicist Georg Simon Ohm discovered that the ratio of voltage to current was constant for most conductors.
Thus Ohm’s Law
V = IR
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Example - Resistance in a car head light
• A car headlight draws 2.5 A of current when connected to the car’s 12 V battery. What is the resistance of the headlight?
• V = IR solve for R R = • Plug in the numbers R = • Solve R = 4.8 Ω
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Resistivity
• The resistance of a particular conductor (wire) depends upon the following:
• Its length – the longer the wire, the greater the resistance.
• Its cross sectional area – the smaller the wire the greater the resistance.
• The material the wire is made of – the higher the resistivity , the greater the resistance.
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Resistivity formula
• R = r (L/A) where• R = resistance ( in ohms)• r = resistivity ( in ohm x meters) • L = wire length• A = cross sectional area• Table 4.3, pg 205 has approximate resistivities
of selected conductors, semiconductors and insulators.
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Example – find the resistance of 100m of No.14 copper wire (1.63mm dia)
• First find the cross sectional area of the wire• = 3.14 ( = 2.09 x • Next, look up the resistivity of copper. From
table 4.3 pg 205, r = 1.7 x * W m• Finally, use the equation,• R = r = (1.7 x * W m)()• R = 0.81 W
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Series circuits
• In a series circuit, there is only one path through the circuit, thus the current through each device in the circuit is the same.
• The total resistance in the circuit is the sum of all the individual resistances.
• The voltage drop across each device is the product of the resistance of the device and the current through it.
• The sum of all the voltage drops across all the devices equals the total voltage of the voltage source (power supply).
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Example series circuit
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Example problem
• In the previous circuit, let Vin = 12V, R1 = 5W, R2 = 10 , W R3 = 15W.
• Find a) the total resistance b) the current in the circuit, and c) the voltage drop across each resistor.
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Part a
• The total resistance is the sum of the individual resistances, thus:
• Rtotal = R1 + R2 + R3 = 5W +10W+15W = 30W
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Part b
• There is only one current in the circuit.• V = IR where R is the total resistance, thus• I = = = 0.4 A
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Part c
• For R1 V = IR = 0.4 A x 5Ω = 2V• For R2 V = IR = 0.4 A x 10Ω = 4V• For R3 V = IR = 0.4 A x 15Ω = 6V• Notice that the total voltage drop ( 2+4+6)
equals the 12V battery in the circuit.
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Parallel circuits
• In a parallel circuit, there are multiple paths through the circuit. The voltage drop across each device is the same and is equal to the power supply.
• The total current in the circuit is the sum of all the individual currents through each device.
• The current through each device is the ratio of the voltage drop across it to the resistance of the device.
• The reciprocal of the total resistance equals the sum of the reciprocals of the individual resistances.
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Example parallel circuit
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Example problem
• In the previous circuit, let V = 12V, R1 = 5W, R2 = 10W
• Find a) the total resistance b) the current in the circuit, and c) the current through each resistor.
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Part a
• Find the total resistance.• • Rtot = = 3.3Ω
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Part b
• Find the current in the circuit• V = 12v and total resistance (part a) = 3.3Ω• V = IR I = • I = = 3.6 A
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Part c
• Find the current through each resistor• R1 V = IR I = = = 2.4A• R2 V = IR I = = = 1.2A• Notice that the total of the individual currents
equals the total current in the circuit.• 2.4A + 1.2A = 3.6A
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Resistors
• A resistor is an electrical device that has a specific resistance.
• The value of the resistance is colored coded.• They are used in circuits to control the current
in a circuit.
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Summary
• Electrical resistance is the opposition to charge flow. The value of resistance is the ratio of voltage to current.
• If a device has constant resistance, it obeys Ohm’s law, V = IR
• The resistance of a wire is given by R = r .• Resistors is series are added to calculate the total
(or equivalent) resistance.• For resistors in parallel, add the reciprocals and then
take the reciprocal of that answer.