Question

Two resistance wires are made of same material and their lengths are equal. If the ratio

of their cross sectional area is 2 : 1, then find the ratio of their resistances​

Answer 1

Answer :-

Ratio of their resistances is 1 : 2 .

Explanation :-

As the length and material of the wire are same, so their resistivity will be also same .

For the 1st wire :-

→ Resistance = R₁

→ Area of cross section = 2A

Equation for resistance becomes :-

⇒ R₁ = ρl/2A ---(1)

For 2nd wire :-

→ Resistance = R₂

→ Area of cross section = A

Equation for resistance :-

⇒ R₂ = ρl/A ----(2)

______________________________

On dividing eq.1 by eq.2, we get :-

⇒ R₁/R₂ = (ρl/2A)/(ρl/A)

⇒ R₁/R₂ = ρl/2A × A/ρl

⇒ R₁/R₂ = 1/2

⇒ R₁ : R₂ = 1 : 2

Answer 2

Given :-

Two resistance wires are made of same material and their lengths are equal. If the ratio of their cross sectional area is 2 : 1

To Find :-

Ratio of resistance

Solution :-

Let the resistance be R an R'

For 1st Wire

ρ = RA/l

ρ = R × 2A/I

R' = ρl/2A

For 2nd wire

ρ = R'A/l

R' = ρl/A

Dividing both sides

(ρl/2A)/(ρl/A) = R/R'

ρl/2A × A/ρl = R/R'

A/2A = R/R'

1/2 = R/R'

Therefore

Ratio is 1:2