Question

Two metal wires have the resistivity 1.62*10^-8 ohm. M and 4.86*10^-8ohm m. Compare the resistance of the two wires if a is twice as long as b and half of its diameter

Answer 1

Answer:

Resistance of A / Resistance of B = 8/3

Explanation:

Resistance is calculated as follows:

Resistance = ρl / A

Where:

ρ is the resistivity of the material

l is the length of the wire

A is the area of the cross-section of the wire

For wire A:

ρ = 1.62 * 10⁻⁸ ohm.M

l = 2l

A = π(r)²

Resistance of A = (1.62 * 10⁻⁸)(2l) / π(r)²

Fore wire B:

ρ = 4.86 * 10⁻⁸ ohm.M

l = l

A = π(2r)²

Resistance of B = (4.86 * 10⁻⁸)(l) / π(2r)²

Now, getting the ratios between the two wires:

A/B = [(1.62 * 10⁻⁸)(2l) / π(r)²] / [(4.86 * 10⁻⁸)(l) / π(2r)²]

A/B = 8/3

Hope this helps :)

Answer 2

Check the ans in this attachment