Find The ratio of resistances of two Cooper Road X and why of lent 30 cm and 10 cm respectively and having radii 2 cm and 1 cm respectively?

Question

Answer

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)� = 4π cm�

similarly, radius of rod y, r₂ = 1cm

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

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

= (l₁/l₂)/(A₁/A₂)

= (30cm/10cm)/(4π cm�/π cm�)

= 3/4

= 3 : 4