Question

find the ratio of resistance of two copper rods x and y of lengths 30cm and 10cm respectively and having radii 2cm and 1cm respectively.

Answer 1

ratio of resistance of two copper rods 3 : 4

it is given that lengths of two copper rods x and y are 30 cm and 10cm respectively and having radii 2cm and 1cm respectively.

we have to find ratio of resistance of two copper rods

we know,

R = ρl/A

where ρ is specific Resistance and it is invariable for the same material, A is cross sectional area and l is length of wire.

here, radius of rod x, r₁ = 2cm

so, Cross sectional area of rod x, A₁ = π(2cm)² = 4π cm²

similarly, radius of rod y, r₂ = 1cm

so, cross sectional area of rod y, A₂ = π(1cm)² = π cm²

now ratio of resistances = R₁/R₂ = (l₁/A₁)/(l₂/A₂)

= (l₁/l₂)/(A₁/A₂)

= (30cm/10cm)/(4π cm²/π cm²)

= 3/4

= 3 : 4

Answer 2

ratio of resistance of two copper rods 3 : 4