How does the resistance of a wire depend on :
(i) Nature of material of wire
(ii) Length of wire
(iii) Area of cross-section of wire
(iv) Temperature of wire
Answers
Explanation:
Cause of Resistance in a Conductor:
Flow of electrons in a conductor is electric current. The particles of conductor create hindrance to flow of electrons; because of attraction between them. This hindrance is the cause of resistance in the flow of electricity.
Resistance in a conductor depends on nature, length and area of cross section of the conductor.
Nature of material: Some materials create least hindrance and hence are called good conductors. Silver is the best conductor of electricity. While some other materials create more hindrance in the flow of electric current, i.e. flow of electrons through them. Such materials are called bad conductors. Bad conductors are also known as insulators. Hard plastic is the one of the best insulators of electricity.
Length of conductor: Resistance R is directly proportional to the length of the conductor. This means, Resistance increases with increase in length of the conductor. This is the cause that long electric wires create more resistance to the electric current.
Thus, Resistance (R) ∝ length of conductor (l)
or R∝lR∝l --------(i)
Area of cross section: Resistance R is inversely proportional to the area of cross section ( A) of the conductor. This means R will decrease with increase in the area of conductor and vice versa. More area of conductor facilitates the flow of electric current through more area and thus decreases the resistance. This is the cause that thick copper wire creates less resistance to the electric current.
Thus, resistance∝1Arearesistance∝1Area of cross section of conductor (A)
Or, R∝1AR∝1A ---------(ii)
From equation (i) and (ii)
R∝lAR∝lA
Or, R=ρlAR=ρlA -----------(iii)
Where ρ (rho) is the proportionality constant. It is called the electrical resistivity of the material of conductors.
From equation (iii)
RA=ρlRA=ρl
Or, ρ=RAlρ=RAl ----------(iv)