Basic Electrical/Resistance/Level-1/Paper-02

Resistance is defined as the property of a substance due to which it opposes  the flow of electricity  through it.Unit ohm  Ω.

Laws of Resistance

(i) Resistance decreases with decrease in   its length, l.

(ii) Resistance decreases with increase in the cross-section A of the conductor.
     i.e. Thicker wire has   lower resistance.

(iii) Resistance depends on the nature of the material the conductor made of.

(iv) Resistance also depends on the temperature of the conductor.

 

          

where ρ is a constant depending on the nature of the material of the conductor and is known as                   its specific resistance or resistivity.Unit ohm-metre(Ω-m).

Conductance :

Conductance (G) is reciprocal of resistance.Unit  siemens (S).
 Earlier, this unit was called mho.

          

 Conductivity :

σ is called the conductivity or specific conductance of a conductor.

It is seen from the above equation that the conductivity of a material is given by

Hence, the unit of conductivity is siemens/metre (S/m).


Effect of Temperature on Resistance

• Insulators (such as paper, rubber, glass, mica etc.) are said to possess a negative temperature-coefficient of resistance 
• Semiconductors have a positive temperature co-efficient of resistance.
• Metals have a positive temperature co-efficient of resistance.
•  The effect of rise in temperature is to decrease the resistance of electrolytes,and partial conductors such as carbon.

Q1. A given wire is stretched to double its length. How much its resistance change ?

(1) resistance is same

(2) resistance becomes four times

(3) resistance becomes two times

(4) resistance becomes half times

Ans: 2
Hint:

After stretching the resistance changes but resistivity remains the same.
As volume of wire is constant so area and length are inversely proportional.

So if the length is doubled by stretching , area of cross section becomes halved.

After stretching wire length is doubled.New length is 2l .

.
Q2. Two cylindrical resistors, R1 and R2, are made of identical material. R2 has twice the length of R1 but half the radius of R1.

Solution:
The area of a circle is equal to the square of its radius times Pi.Relationship between the cross section  area of half the radius of R1 with R2.

Resistance is inversely proportional to the area of cross section.