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Resistance

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Overview

The resistance of a conductor can be defined as the property of the conductor that opposes the flow of electric current through it. This note provides information about resistance, factor affecting resistance, resistivity and conductivity.
Resistance

Resistance

The resistance of a conductor can be defined as the property of the conductor that opposes the flow of electric current through it. The SI unit of resistance is ohm. It is denoted by the upper case letter 'R'. When an electric current of 1 Ampere passes through a conductor, then the potential difference becomes 1 volt, this resistance of a conductor is known as 1Ω (ohm).
Metals like silver, copper, gold etc. have low resistance. Copper is used mostly in the wire as it offers low resistance. Some substances offer very high resistance. Some mostly used substances are given below with their composition, uses and resistance,

Names of Substances Composition (Alloy) Uses Resistance at 20 degree celsius ohm metres
Constantan 55% copper and 45% nickel Used in construction of pyrometer and thermocouple 5 \(\times\) 10-7
Manganin 83% copper, 13% manganese and 4% nickel Used in the construction of rheostats and resistors 4.2 \(\times\) 10-7
Nichrome 60% nickel and 40% chromium Used in construction of heating element of heaters 1.1 \(\times\) 10-6
Factors affecting resistance
  1. When we measure the resistance for two different lengths of wire having same cross section area, the resistance of the long wire is higher than short wire. The resistance of a conductor is directly proportional to its length. Longer the length of wire, greater will be the resistance. i.e. R∝ l
  2. When we measure the resistance of two wire of the same length but different cross section area, we find thin wire has high resistance than the thicker one. The resistance of a conductor is inversely proportional to its cross- section area of the conductor. i.e. R∝ \(\frac{1}{A}\)
  3. The resistance of the conductor also depends on its material which it is made of. Conductors of same length and size have different resistance if they are made of different materials.
  4. The temperature also determines the resistance of the conductor.Resistance is directly proportional to the temperature of the conducting wire. The resistance of a conductor increases with increase in temperature.

Resistivity and conductivity

As we know that, the resistance of a conductor is directly proportional to its length and inversely proportional to its cross- sectional area. If 'l' is the length of a wire, 'A' is it's the cross- sectional area and 'R' is its resistance, then

R∝ l ........... (i)

R∝ \(\frac{1}{A}\) ................(ii)

From eq (i) and (ii) we have

R∝ \(\frac{l}{A}\)

∴ R =ρ \(\frac{l}{A}\)

Where,
ρ (Rho) = resistivity or specific resistance of the material
The SI unit of resistivity (ρ) is ohm- metre (Ωm).

If l = 1m, A = 1m2, then R =ρ

ρ = R \(\frac{A}{l}\).

The resistivity of a material is numerically equal to the resistance of a conductor of unit area per unit length of a material.

The reciprocal of the resistivity (ρ) of a material is called its conductivity (σ) sigma.

Conductivity (σ) =\(\frac {1}{ resistivity (ρ)}\).

Things to remember
  • The resistance of a conductor can be defined as the property of the conductor that opposes the flow of electric current through it. 
  • The resistance of a conductor is directly proportional to its length.
  •  The resistance of a conductor increases with increase in temperature.
  • The resistivity of a material is numerically equal to the resistance of a conductor of unit area per unit length of a material.
  • The reciprocal of the resistivity (ρ) of a material is called its conductivity (σ) sigma.
  • It includes every relationship which established among the people.
  • There can be more than one community in a society. Community smaller than society.
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Resistance
Questions and Answers

Any two differences between conductor and insulator are as follows,

Conductor Insulator
Those substances that allow heat and electricity to flow through them are called conductors. Those substances that do not allow heat and electricity to flow through them are called insulators.
There are free electrons. There are not free electrons.
Eg: brass, copper, silver etc Eg: silk, rubber etc.

The resistance of a conductor depends on the following factors:

  • Length of the conductor
  • Cross- sectional area of the conductor
  • Material of which the conductor is made
  • Temperature of the conductor
  • Shape of the conductor
The resistance of a conductor is its property that restricts the movement of free electrons through it.
The SI unit of resistance is ohm (?).
Insulators are those substances which do not have free electrons and does not pass electric current through it.
Any two examples of conductors are copper and iron.
If a current of 1A passes through a conductor maintains a p.d. of 1V across its ends, then its resistance is called 1 ohm.
The reciprocal of the resistivity of a material is called its conductivity.
The SI unit of conductivity is ?-1m-1 (Perohm per meter).
The resistance of a conductor is directly proportional to the temperature.
The resistance of a conductor is directly proportional to its length.
Conductors are those substances which have free electrons and can conduct electricity through them.
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