Resistance

This is a measure of a materials opposition to the flow of current through it. Unit: Ohms ( Ω )

It is caused by collisions between the electrons and the atoms in the wire. The hotter the wire, the more chance there is of a collision. Therefore hot wires have more resistance.

Resistance (ohms) = potential difference (volts) current (amps ) In physics code we write this as R = V/I

Ohmmeter This is an instrument to measure resistance.

A Rheostat A rheostat is a variable resistor. This means that you can change its resistance.

Variable Resistance If you can can control or change the resistance you can control the amount of current flowing in the circuit.

Resistance v Current When Resistance is high, Current is low. When Resistance is low, current is high. law/ohms-law_en.html law/ohms-law_en.html

Ohms Law States that the current flowing in a metallic conductor is proportional to the voltage across it, provided the temperature remains constant.

Resistors in Series R Total = R 1 + R 2

Derivation:

Resistors in Parallel

Derviation

Test your learning A circuit consists of a 3 Ω resistor and a 6 Ω resistor connected in parallel to a 1.5 V d.c. supply as shown. Calculate the total resistance of the two resistors. Calculate the current flowing in the circuit. What is the current in the 3 Ω resistor? The diagram shows a number of resistors connected to a 12 V battery and a bulb whose resistance is 4 Ω. Calculate the combined resistance of the 15 Ω and 30 Ω resistors in parallel. Calculate the total resistance of the circuit Calculate the current flowing in the circuit

Factor affecting resistance of a conductor Temperature Length Crosssectional area Material from which it is made

Dependence of resistance on temperature The resistance of a metallic conductor increases as the temperature increases The resistance of most other substances decreases as the temperature increases

For a metallic conductor The resistance changes linearly with temperature (as free elctrons collide more frequently with atoms due to vibration)

For Insulators and Semiconductors The resistance of an insulator or semiconductor decreases as the temperature increases. (As a result of the increased number of conducting electrons as a result of vibration)

The thermistor Thermal Resistor Is a semiconductor whose resistance increases rapidly with increasing temperature

Resistivity Resistivity is defined as the resistance of a cube of material of side one metre. or Resistivity is defined as the resistance of a material of unit length and unit cross sectional area. The symbol for resistivity is  (pronounced “rho”).

The resistance of a conductor is the ratio of the PD across it to the current flowing through it

R=V/I

Factors affecting the resistance of a conductor Temperature Length Cross-sectional area The material from which its made

Temperature The resistance of a metal conductor increases as temperature increases The resistance of other materials (eg carbon and semiconductors) decreases as the temperature increases.

Metallic Conductor - Eg Copper In copper, there are usually one free electron from every copper atom. The movement of this these electrons through the metal is an electric current. As the electrons move they collide with atoms. This is the resistance to the electrons motion. The greater the collisions, the greater the resistance.

When the heat gets turned up.. The metal atoms vibrate at a greater rate. Electrons trying to move through incur more collisions with the atoms......more RESISTANCE

The resistance changes linearly with Temperature. T (C’) R (ohms) 0’C

Insulator and Semiconductors Most electrons are attached to atoms. Few free electrons.

When the heat gets turned up.. Electrons are freed from atoms. These electrons can form an electric current. The resistance of an insulator or semiconductor decreases as the temperature increases.

Resistivity Resistivity is defined as the resistance of a cube of material of side one metre. or Resistivity is defined as the resistance of a material of unit length and unit cross sectional area. The symbol for resistivity is  (pronounced “rho”). The unit of resistivity is the Ωm

The resistance of a conductor depends on: Length Cross-sectional area Material from which its made

Resistivity and length The resistance of a uniform conductor is directly proportional to its length

Resistance and cross section area If the cross-sectional area is doubled the resistance is halved

Resistivity and material The constant of proportionality If the material is a good conductor is small If the material is a bad conductor is large

Therefore resistivity: To do these you should revise how to convert from millimetres square to metres square. See the diagram on page 6 for a reminder.

Example What length of copper wire of cross section area 2mm 2 is needed to make a resistor of resistance 10Ω if the resistivity of copper is 1.7 x Ωm.

Example A coil of copper wire 20m long has a uniform cross-sectional area. The diameter of the wire is 0.055mm. Taking the resistivity of copper to be 1.7 x 10-8Ωm. Calculate the resistance of the coil.

Measuring resistivity of a sample When given d (diameter) you must calculate cross-sectional area How?! A=∏r 2

See Exp Sheet

Pg 269

2008 A toaster has a heating coil made of nichrome which it has a resistance of 12 Ω. The coil is 40 m long and it has a circular cross- section of diameter 2.2 mm. Calculate the resistivity of nichrome.

Measuring Resistance using a Wheatstone bridge A Wheatstone Bridge can be used to find the resistance of an unknown resistor.

The values of the four resistors are arranged – by trial and error – so that no current flows in the galvanometer. (The bridge is now said to be balanced). It can be shown that the relationship between the resistors is

Therefore knowing the values of any three resistors allows us to calculate the fourth. When using this formula make sure that the resistors are arranged as shown.

The metre bridge

This is similar in principle to the Wheatstone bridge, except two of the resistors are replaced by a single strip of uniform-resistance wire, and because resistance is proportional to length the balance point can be reached by simply sliding the contact wire along this lower uniform- resistance wire. One of the resistors is known and the two lengths can be measured (either side of the contact point). The unknown resistance can then be found using the formula

A metre bridge was used to measure the resistance of a sample of nichrome wire. The diagram indicates the readings taken when the metre bridge was balanced. Calculate the resistance of the nichrome wire   R = 7.86 Ω

Uses Remember that the bridge above was balanced to begin with, so no current flows through the galvanometer. Now if the temperature of one of resistors is changed for any reason, current will flow through the galvanometer. This current can be used to activate a second circuit such as a heater or an alarm. Examples Temperature Control A Fail-Safe Device

The Thermistor Thermal resistor A thermal resistor is a semi-conductor whose resistance decreases rapidly with increasing temperature.