Question

The ratio of length of two wires of some substance is 2:3 and the ratio of their diameter be 1:2.Calculate the ratio of resistivity.

Answer 1

Answer:

Final Answer : 9:16

Steps:

1) We know that the Resistance of a same wire is proportional to (l/A) .

where L = Length of wire,

A = Area of cross section

And, Area is proportional to d^2 ,

where 'd' is diameter of wire.

=> Resistance is proportional to

\frac{l}{ {d}^{2} }

2) We have,

Ratio of their length = 1:2

Ratio of diameters = 2:3

=> Ratio of Area of cross- section = 2^2:3^2 = 4:9

=> Ratio of resistance :

\frac{1}{4} \: to \: \: \frac{4}{9} \\ = > 9 \: to \: 16

9:16

3) Since, current in series circuit is same.

=> Ratio of Potential difference across wires :

R(1) : R(2) = 9:16

Hence, Required Ratio is 9:16