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

Answer 1

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Answer 2

Given:

ratio of electron density = 1 : 3

To Find:

ration of resistance

Solution:

we know,

ρ = m/ηe²ζ

ρ = resistivity

η  = electron density

clearly,

ρ ∝ 1 / η

R = ρl / A

also,  R  ∝ ρ  ( Directly proportional )

⇒ R ∝ 1 / η ( inversly proportional )

⇒ Ra / Rb =  ηb /  ηa

⇒ Ra / Rb = 3 / 1

So, Ra : Rb = 3 : 1.