The resistance of a wire of 0.01 cm radius is 10 Ω. If the resistivity of the material of the wire is 50 × 10-8 ohm meter, find the length of the wire.

Sure, I can help with that. The resistance (R) of a wire can be found using the formula:

R = ρL/A

where:

• R is the resistance,
• ρ is the resistivity of the material,
• L is the length of the wire, and
• A is the cross-sectional area of the wire.

We can rearrange this formula to solve for L:

L = R * A / ρ

The cross-sectional area (A) of a wire can be found using the formula for the area of a circle (since the wire is cylindrical), which is:

A = πr²

where r is the radius of the wire. In this case, the radius is 0.01 cm, which is 0.0001 m (since 1 cm = 0.01 m). So:

A = π * (0.0001 m)² = 3.14159 * 10^-8 m²

Now we can substitute R = 10 Ω, A = 3.14159 * 10^-8 m², and ρ = 50 * 10^-8 Ωm into the formula for L:

L = 10 Ω * 3.14159 * 10^-8 m² / 50 * 10^-8 Ωm = 0.628318 m

So, the length of the wire is approximately 0.628318 meters.