Colour coding of resistors, resistivity of various materials, practice problems, FAQs

You take a battery, some copper wires, a bulb and complete the circuit. You notice that the bulb glows brightly. The same happens when you connect a silver wire; the bulb glows with good intensity. Now replace the copper wires with a plastic wire; you would notice that the bulb did not glow at all. Why? This is because metals like copper,silver, aluminium are said to be good conductors; meaning that they allow almost all electrons to pass through them. The plastic wire, on the other hand, called an insulator, blocks electron flow, hence the bulb does not glow. The ability to block current is called resistance of a material. It arises due to the fact that electrons collide with the ions in its lattice. The terms resistance and resistivity are closely related. If you’ve ever been to a physics lab, you would notice tiny capsule shaped structures called resistors lying around; they are used in remote controls, refrigerators,etc. In this article, we will explore more about resistors and resistivity. 

Table of contents 

• Resistors
• Resistance and resistivity
• Resistivity, relaxation time, drift velocity.
• Resistivity values for various materials
• Colour code mnemonics 
• Practice problems
• FAQs

Resistors

A resistor is a component with electrical resistance. The resistance of a resistor is measured in Ohms; the colour bands on the resistor each carry a unique digit that helps us to find out its resistance. 

Resistance and resistivity

The resistance of a conductor ( is related to its resistivity( as ; where denotes the length of the conductor (unit-) and denotes the area of the cross section(square metres-. For a material with unit length and area of cross section . i.e the resistance is equal to the resistivity of a material that has unit area and unit length. For metals, both the resistance and resistivity increase with increase in temperature. 

  , Volume of the conductor

; Mass of the conductor, Density

For the two wires of the same material, and density remains constant. 

∴

The unit of resistance is The unit of resistivity is

Resistivity, relaxation time, drift velocity.

When a voltage is applied in between the terminals of a conductor of area , the current starts flowing in it; the velocity with which electrons get drifted from one point to another is called drift velocity( If is number of charges per unit volume in the conductor, and is the electronic charge, contributing to the flow of a current then 

is called current density. It gives an idea about current flowing per unit given area. 

Also, relaxation time the time between two consecutive collisions of electrons.

Now acceleration (-Electric field)

where is called the electrical conductivity of the material. Higher the conductance, higher is its ability to let current flow through it. 

Note:

Resistivity values for various materials

Depending upon their ability to conduct electricity, materials are broadly classified into three- Conductors, semiconductors, insulators. Conductors have low values of resistivity; insulators, like rubber, which are poor conductors, have high resistivity values. Semiconductors have resistivity that lies in between that of conductors and insulators. 

Type of material	Example	Resistivity values
Conductors	Copper	to
Semiconductors	Germanium	to
Insulators	Plastic	to

Colour code mnemonics

The bands on a resistor are known as its colour codes.The colour codes signify the resistance of the resistor. In the following figure, four bands are observed; each colour carries a unique digit known as mnemonics, which is depicted in the table below. 

Colour	Digit	Multiplier	Tolerance
Black	0
Brown	1
Red	2
Orange	3
Yellow	4
Green	5
Blue	6
Violet	7
Grey	8
White	9
Gold
Silver
No colour

In the given example, the resistance of the carbon resistor can be calculated following the mnemonics: 

Digit Brown Code 

Digit Black Code 

Digit (Multiplier)Orange Code 

Digit (Tolerance)Gold Code

Hence .

Note

Practice problems

Q. A resistor is found to have a resistance of What are its respective colors?

A. Given resistance The number corresponds to orange , corresponds to violet, multiplier of corresponds to red, and a tolerance of corresponds to silver. Hence the colours of the resistor are Orange, Violet, Red, Silver. 

Q. A resistor has the following colours: brownred green gold. Its resistance, in Ohms, is

(a) (b) (c)

(d)

A. d

Brown

Red

Green (Multiplier)

Gold (Tolerance)

Hence the resistance of the conductor

Q. If and indicate the relaxation time, electronic charge and mass . The resistance of a conductor having length and area would be 

(a) (b) ( c ) (d)

A. a

Resistance where resistivity

Substituting the value of resistivity in resistance, we get

Q. The resistance of a wire was initially calculated to be Keeping its volume constant, the wire is stretched to twice its initial length. Its resistance now is Then 

(a) (b) (c) (d)

 A. b

We have resistance where is the volume of the wire and is the length of the wire. When the conductor is stretched, 

FAQs

Q. Write the definition of 1 ohm?
A. when ohm. If then  

1 ohm is the resistance of a conductor which allows a current of to flow through it when a potential difference of 1 volt is applied between its ends.

Q.What does a resistor mean?
A. A resistor is the one whose resistance is

Q. How does resistivity vary with temperature for metals?
A. With increase in temperature, the resistivity of metals increases.

Q. How does resistivity vary for semiconductors?
A. For semiconductors, the resistivity decreases as temperature increases.