Question

The resistance of a conducting wire is 10 ohms. If the length of this wire is doubled and the area of cross section is halved, then what will be the resistance of this wire

Answer 1

Answer:

40

Explanation:

old resistance = kL/A

newresistance = 2kL÷A/2 = 4kL/A = 40 ohm

Answer 2

resistance of wire will be 40Ω.

initial resistance of wire, R_i = 10Ω

let length of wire is l and cross Section area of it is a.

then , R = ρ l/a , where ρ is resistivity of material of the wire.

so, 10Ω = ρ l/a .........(1)

a/c to question,

new length of wire, l' = 2l

new cross sectional area of wire, a' = a/2.

so, R' = ρ l'/a'

= ρ (2l)/(a/2)

= ρ 4l/a

= 4 ρ l/a

from equation (1),

R' = 4R = 40Ω

hence, new resistance of wire will be 40Ω

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