Respuesta :
Answer:
Length = 2.453 m
Explanation:
Given:
Resistivity of the wire (ρ) = 1 × 10⁻⁶ Ω-m
Diameter of the wire (d) = 0.250 mm = 0.250 × 10⁻³ m
Resistance of the wire (R) = 50 Ω
Length of the wire (L) = ?
The area of cross section is given as:
[tex]A=\frac{1}{4}\pi d^2\\\\A=\frac{1}{4}\times\ 3.14\times (0.250\times 10^{-3})^2\\\\A=0.785\times 6.25\times 10^{-8}\\\\A=4.906\times 10^{-8}\ m^2[/tex]
We know that, for a constant temperature, the resistance of a wire is directly proportional to its length and inversely proportional to its area of cross section. The constant of proportionality is called the resistivity of the wire. Therefore,
[tex]R=\rho \frac{L}{A}[/tex]
Expressing the above in terms of length 'L', we get:
[tex]L=\frac{RA}{\rho}[/tex]
Plug in the given values and solve for 'L'. This gives,
[tex]L=\frac{50\times 4.906\times 10^{-8}}{1\times 10^{-6}}\ m\\\\L=\frac{2.453}{1}=2.453\ m[/tex]
Therefore, length of No. 30 wire (of diameter 0.250 mm) is 2.453 m.
