Question

If two conducting wires A and B of same dimensions have electron density ratio 1:3. If their relaxation time is same then the ratio of resistance of A to resistance of B is

A)1:1

B)3:1

C)1:3

D)9:1​

Answer 1

Answer:

C)1:3

Explanation:

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Answer 2

Answer:

The ratio of the resistance of A to the resistance of B is 3:1 i.e.option (B).

Explanation:

The resistivity of a material is given as,

$\rho=\frac{m}{ne^2\tau}$       (1)

Where,

ρ=resistivity of the material

m=mass of an electron

n=electron density

e=charge on an electron

τ=relaxation time

So, equation (1) can also be written as,

$\frac{\rho_A}{\rho_B}=\frac{n_B}{n_A}$         (2)

And we know that the resistance of the wire is directly proportional to the resistivity of the wire i.e.

$R\propto \rho$

$\frac{R_A}{R_B} =\frac{\rho_A}{\rho_B}$        (3)

From the question we have,

$\frac{n_A}{n_B}=\frac{1}{3}$       (4)

By using equations (2) and (4) in equation (3) we get;

$\frac{R_A}{R_B} =\frac{3}{1}$

Hence, the ratio of the resistance of A to the resistance of B is 3:1 i.e.option (B).