Question

ASSERTION : Resistivity of the wire increases with the increase in the
temperature of the wire.
REASON : Resistivity of a wire depends on the dimensions of the wire.

Answer 1

Answer- The above question is from the chapter 'Electricity'.

Let's know about resistance and resistivity.

Resistance- It is the property of a conductor, semi-conductor or insulator to resist the flow of charges.

R = V/I

where R = Potential difference between two end points and I = flow of current.

Resistance is generally measured in Ohms. (Ω)

R = $\frac{\rho l}{A}$

where ρ = resistivity, l = length of material and A = area of material.

R ∝ l

R ∝ ρ

R ∝ 1/A

R ∝ Temperature

Resistivity- It is the materialistic property of a conductor which tells the strength of resistance.

It is denoted by ρ.

ρ ∝ Temperature

ρ is independent of length and area.

Given question:

ASSERTION: Resistivity of the wire increases with the increase in the

temperature of the wire.

REASON: Resistivity of a wire depends on the dimensions of the wire.

Point out if:

   (a) Both, A and R, are true and R is the correct explanation of A.

   (b) Both, A and R, are true but R is not the correct explanation of A.

   (c) If A is true but R is false.

   (d) If A is false but R is true.

Answer: We know that ρ ∝ Temperature.

So, ASSERTION is True.

We also know that ρ is independent of its dimensions.

So, REASON is also False.

But REASON is not the correct explanation of ASSERTION.

∴ (c) A is true but R is false.

Answer 2

The assertion in the following question is true but the reason mentioned is wrong.

Explanation:

• The temperature coefficient of resistance is the change in resistance of the material per unit change resistance and change in temperature.

            Mathematically,  $R=R_{o}(1+\alpha (T-T_{o} ))$     $(i)$

                                  and $\alpha = \frac{R-R_{o} }{R_{o}(T-T_{o} ) }$        $(ii)$

• According to Ohm' s law, we know that

            $R$ ∝ ρ   $;$ where ρ is the resistivity of the material.

• Resistivity of a material is the opposition offered by a conductor to the flow of current. It depends upon the quality of the material of the conductor and hence is mainly qualitative.

       Substituting this value in $(i)$, we get

                              ρ = ρ₀(1 + α (T - T₀))

We can clearly see that ρ ∝ T  ; resistivity is directly proportional to the temperature.

Hence, the resistivity of a material increases with increase in temperature.

• This is mainly because when a lot of current flows in the circuit, a great number of collisions of the electrons takes place in the the conductor due to which relaxation time that is the time between two successive collisions in a conductor reduces.

• This accumulation of huge number of electron collision taking place increases the temperature of the conductor and a situation similar to a traffic jam is created hence the resistance and resistivity of the conductor is also reduced.

• Also we can see that the only factor on which resistivity ρ of a material is depended is the initial resistivity and the temperature.

• Hence, Resistivity of a material is not depended upon the dimension of the material.