Two wires A and B of same material and of different lengths have different resistance Calculate the ratio of their lengths, if radius of A as double the radius of B..
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R ∝ l/A
Ra = ρ la/Aa
Rb = ρ lb/Ab
Ra = Rb
Ab = A
Aa = 4A
Ra = la/4A
Rb = lb/A
(Neglecting rho because it is equal because they are made up of same substance)
Ra = Rb = R
4R = la --- Eq.1
R = lb --- Eq.2
Eq.1/Eq.2
la/lb = 4/1
Therefore,
la : lb :: 4 : 1
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