Question

Two wires of same material have lengths l and 2L and cross sectional areas 4A and a respectively . Then what would be the ratio of their resistances

Answer 1

The ratio between their resistances is 8:1

Explanation:

Cross sectional area of wire A = 4A

Cross sectional area of wire B = a

Specific resistance "ρ" = R x A /L

For wire A

"ρ" = R x A /L

"ρ" = R x 4πr^2 /L

For wire B =  "ρ" = R x A /L

"ρ" = R x πr^2 /2L

By comparing

R x 4πr^2 /L = R x πr^2 /2L

4 /L = 1 /2L

4 = 1/2

8 = 1

Thus the ratio between their resistances is 8:1

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