Question

Two wires A & B are of same metal have same area of cross-section and have
their lengths in the ratio 2:1. What will be the ratio of currents flowing through
them when the same potential difference is applied across the length of each of
them?
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Answer 1

resistance is given as

R = ρL/A

here ρ = resistivity of wire , L = length of wire , A = area of cross-section

clearly , resistance is directly propotional to length of wire

L₁ = length of one wire  , L₂ = length of one wire

R₁ = resistance of one wire , R₂ = resistance of one wire

so R₁/R₂ = L₁ / L₂

we have been given that ,  L₁ / L₂ = 2/1

so  R₁/R₂ = 2/1

V₁ = potential difference in one wire = V₂ = potential difference in other wire

i₁ R₁ = i₂ R₂

i₁ /i₂ = 1/(R₁/R₂)

i₁ /i₂ = 1/(2/1)

i₁ /i₂ = 1/2

so ratio of currents 1:2