Specific resistance of the material of a wire using a meter bridge 

Specific resistance of the material of wire is an important topic of electric current. It is important to have a very good understanding of resistance in order to understand specific resistance. It is vital for the JEE aspirants to have good grip on the topic in order to remain competitive in the JEE. We first discuss resistance and then we will move on specific resistance:

Resistance:

When the electrons travel through wires, they experience some sort of hindrances in their way. Resistance, as the name suggests is the hindrance or the obstruction in the flow of charge. When an electron moves from one terminal to another, its way is not direct. In fact, it is a diverted path, which includes various collisions encountered with fixed atoms within the conductor. The electric potential established across the two conductors encourages the charge, it is the resistance that discourages or disrupts it.

Resistance


Specific Resistance:
The Specific resistance of a material is the resistance offered by a one foot long wire of the material with a diameter of one MIL. There is a close relationship between the resistance and specific resistance of the material. The resistance of a wire is directly proportional to the specific resistance of the material. The specific resistance of a material is denoted by the letter ‘K’.   

We list below various materials along with their specific resistance:

Material

         "K"

      Material

     "K"

Brass

          43.0

      Aluminum

     17.0

Constantan

          295

      Monel

      253

Copper

          10.8

      Nichrome

      600

German Silver 18 %

          200

      Nickel

      947

Gold

          14.7

      Tantalum

      93.3

Iron (Pure)

          60.0

      Tin

      69.0

Magnesium

          276

      Tungsten

      34.0

Manganin

          265

       Silver

      9.7

Variables affecting Electrical Resistance:

Electrical resistance is affected by various factors. The resistance to the flow of charge in an electric circuit is the same as the resistance in the water and pipe surfaces as a result of friction or the resistance offered by obstacles. Just like the water flow, the net quantity of resistance to charge flow within a wire of an electric circuit is affected by various factors like:

  1. The amount of resistance will obviously depend on the total length of the wire. There is a direct relationship between the amount of charge and the length of wire. The longer the wire, higher is the rate of electric charge. The simple reason behind this is that in case of a longer wire, there are more chances of collisions between the charge carriers and the atoms of the wire.
  2. The cross-sectional area also affects the intensity of resistance. If the wire is wide, it is obvious that there will be less resistance to the flow of charge in the wire. When all the other variables or attributes are constant, the rate of flow of charge is higher in wider wires exhibiting greater cross-sectional areas.
  3. Resistance is also affected by the material of the wire. Different materials have different conductive ability. If the material is a good conductor, it will offer less resistance to the flow of charge. The ‘resistivity’ of  a material denotes its conducting ability. 

View the following video for more on resistance and resistivity

Specific resistance of materials:

We discuss some of the basic facts of specific resistance:

  • The specific resistance of materials is independent of length and cross-sectional area.
  • Specific resistance is a constant entity. Its value remains constant for every individual substance.
  • Any sort of change in length or cross-sectional area may bring about a change in the resistance of a wire as we have the relation R= pL /A, where p is the specific resistance. But, the specific resistance of the wire in all above conditions is same. Only a change in temperature can bring about a change in the specific resistance.
  • Whenever there is a change in area or length, it brings about a corresponding change in R in such a way that specific resistance ‘p’ always remains constant.   

To find resistance of wire using meter bridge:

We now try to find resistivity using Meter Bridge. A known length (L) of a wire is connected in one of the gaps (P) of a meter bridge, while a ‘resistance box’ is inserted into the other gap (Q). The circuit is completed by using a battery (B), a rheostat (Rh), a key (K) and a galvanometer (G). consider the figure given below to get a better picture of the 

Specific Resistance of MaterialThe balancing length ‘l’ is found by closing key K and momentarily connecting the galvanometer until it gives zero deflection (null point). Then,  

p / q =  / 100 –  (using the expression for the meter bridge at balance)

[Here, P represents the resistance of the wire while Q represents the resistance in the resistance box. The key K is kept open when the circuit is not in use.]

The resistance of the wire, P = r L / πr2 or r = πr2 / L .P

where r is the radius of the wire and L is the length of the wire (r is measured using a screw gauge while L is measured with a scale).

askIITians offers detailed study material which contains all the important topics of IIT JEE Physics. The content covers all the important questions like how is a galvanometer connected in a meter bridge or how to find specific resistance using Meter Bridge.  

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