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.
Question
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.
Solution
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.
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