Question

The resistance of a wire of length 250 m is 1 ohm. If the resistivity of the material of wire is 1.6

x 10–8

ohm meter, find the area of cross-section of the wire. How much does the resistance

change if the diameter is doubled?

Answer 1

The information provided in the question is as follows:
Length of wire, l250 m

Resistance of wire, R1 Ω

Resistivity of wire, ρ1.6×10-8 Ω m

The resistance is given as:

R=ρlA⇒1=1.6×10−8×250A

⇒A=1.6×10−8×250

=4×10−6 m2A=π(d2)2

When the diameter is doubled, then
A'=π(d'2)2
=π(2d2)2
=4π(d2)2
=4A

Keeping the same length, the resistance of the wire,
R'=ρlA'
=>14ρlA
=>R4=14
=0.25 Ω

Answer 2

hey bro/gal.

since, resistance = resistivity× length / area

=) 1 = 1.6 * 10^-8 * 250/ A

=) A = 400*10^-8 = 4*10^-6 m²

=) if diameter is doubled then area will become 4A.

=) new Area = A' = 4*4*10^-6 = 16*10^-6 m²

=) R' = 1.6*10^-8 * 250/ 16*10^-6

= 1/4 ohm.