Question

A wire of cross-sectional area 5.00 106 m2 has a resistance of 1.75 O. What is the resistance of a wire of the same material and length as the first wire, but with a cross-sectional area of 8.75 106 m2

Answer 1

Answer:

the resistance of the second wire is 1 ohm.

Explanation:

Given;

cross sectional area of the first wire, A₁ = 5.00 x 10⁶ m²

resistance of the first wire, R₁ = 1.75 ohms

cross sectional area of the second wire, A₂ = 8.75 x 10⁶ m²

resistance of the second wire, R₂ = ?

The resistance of a wire is given as;

R ∝ $\frac{L}{A}$

Since the length of the two wires is constant

R₁A₁ = R₂A₂

$R_2 = \frac{R_1A_1}{A_2} \\\\R_2 = \frac{1.75\ \times \ 5.00\times 10^6}{8.75\times 10^6} \\\\R_2 = 1 \ ohm$

Therefore, the resistance of the second wire is 1 ohm.