Question

The resistance of a wire of length 250 m is 1 ohm if the resistivity of the material iof wire is 1.6×10 raise to power minus 8 ohmmeter.find the area of cross section of the wire.How much does the resistance change if diameter is doubled

Answer 1

Length of wire ,L = 250m
resistance of wire , R = 1Ω
resistivity of material of wire , ρ = 1.6 × 10⁻⁸ Ωm

Now,use the formula
R = ρL/A , here A is cross section area
A = ρL/R
= 1.6 × 10⁻⁸ × 250/1
= 4 × 10⁻⁶ m²

Now, diameter of wire is doubled then resistance = ?
Actually, R is inversely proportional to square of diameter [∵ R $\propto$1/A , R $\propto$ 1/πd²/4 or R $\propto$1/d²]
Now, if diameter is doubled then resistance will be 1/4th .
So, resistance = 1/4Ω = 0.25Ω

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.