Question

TWO CONDUCTORS A AND B have their lengths in ratio 4:3 and their area of cross section in ratio 1;2 resistivities in ratio 2:3 then what is ratio of their resistances

Answer 1

Given :-

• Ratio of lengths of two conductors A and B is 4 : 3
• Ratio of corresponding area of cross section is 1 : 2
• Ratio of corresponding resistivity is 2 : 3  

To find :-

• Ratio of their resistances

Formula used :-

• R = ρ l / A

( where R is the resistance , ρ is resistivity , l is length and A is area of cross section of conductor )

Solution :-

Let, length of A and B be l₁ and l₂

area of cross section be A₁ and A₂

resistivity be ρ₁ and ρ₂  respectively.

and Resistances of conductor A and B be R₁ and R₂ respectively .

then,

→ R₁ / R₂ = ( ρ₁ l₁ / A₁ ) / ( ρ₂ l₂ / A₂ )

→ R₁ / R₂ =  ( ρ₁ l₁ / A₁ ) × ( A₂ / ( ρ₂ l₂ ) )

→ R₁ / R₂ = (ρ₁ / ρ₂) × (l₁ / l₂) × (A₂ / A₁)

using the given information

→ R₁ / R₂ = ( 2 / 3 ) × ( 4 / 3 ) × ( 2 / 1 )

→ R₁ / R₂ = 16 / 9

Therefore,

Ratio of their Resistances is 16 : 9 .