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MaRussiya [10]
3 years ago
10

Nichrome wire, often used for heating elements, has resistivity of 1.0 × 10-6 Ω ∙ m at room temperature. What length of No. 30 w

ire (of diameter 0.250 mm) is needed to wind a resistor that has 50 ohms at room temperature?
Physics
1 answer:
worty [1.4K]3 years ago
4 0

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:

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

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,

R=\rho \frac{L}{A}

Expressing the above in terms of length 'L', we get:

L=\frac{RA}{\rho}

Plug in the given values and solve for 'L'. This gives,

L=\frac{50\times 4.906\times 10^{-8}}{1\times 10^{-6}}\ m\\\\L=\frac{2.453}{1}=2.453\ m

Therefore, length of No. 30 wire (of diameter 0.250 mm) is 2.453 m.

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