Question

Compare the resistance of two wires of same material. Their lengths are in the ratio 2 : 3 and their diameters are in the ratio 1 : 2.

Answer 1

Answer:

R1, R2=8:3

Explanation: Given,

The resistance of the wire is given by:

R = ρ L/A

'L' is the length of wire

'A' is the area of cross-section

The length of two wires of the same material are in ratio 2:3 and their diameters are in ratio 1:2. Let R₁ and R₂ are the resistance of two wires.

SO, R1 = ρ  LI/$\pi$(d1/2) ^2..........(1)

R2 = ρ L2/$\pi$(d2/2)^2.............(2)

Dividing equation (1) and (2) :

R1/R2 =L1/L2×(d1/d2)^2

l₁ : l₂ = 2 : 3

d₁ : d₂ = 1 : 2

So, R1/R2=2/3×(2/1)^2

R1/R2=8/3

So, the resistance of two wires of the same material is in the ratio of 8:3.

If you didn't understand let me I will post a picture of the sum solved in a book.  

Answer 2

Explanation:

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