Resistance in Electrical Systems

Chap 4.3

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.

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.

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.

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.

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.

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.

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

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

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.

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.

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

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).

Example series circuit

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.

Part a

• The total resistance is the sum of the individual resistances, thus:

• Rtotal = R1 + R2 + R3 = 5W +10W+15W = 30W

Part b

• There is only one current in the circuit.• V = IR where R is the total resistance, thus• I = = = 0.4 A

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.

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.

Example parallel circuit

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.

Part a

• Find the total resistance.• • Rtot = = 3.3Ω

Part b

• Find the current in the circuit• V = 12v and total resistance (part a) = 3.3Ω• V = IR I = • I = = 3.6 A

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

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.

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.