Question

b) 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 wire?​

Answer 1

Answer:

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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