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:
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,
Expressing the above in terms of length 'L', we get:
Plug in the given values and solve for 'L'. This gives,
Therefore, length of No. 30 wire (of diameter 0.250 mm) is 2.453 m.