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Lelechka [254]
3 years ago
6

A carbon rod with a radius of 1.9 mm is used to make a resistor. What length of the carbon rod should be used to make a 3.7 Ω re

sistor? The resistivity of this material is 1.8 × 10−5 Ω · m .
Physics
1 answer:
vladimir2022 [97]3 years ago
5 0

Answer:

Length = 2.32 m

Explanation:

Let the length required be 'L'.

Given:

Resistance of the resistor (R) = 3.7 Ω

Radius of the rod (r) = 1.9 mm = 0.0019 m [1 mm = 0.001 m]

Resistivity of the material of rod (ρ) = 1.8\times 10^{-5}\ \Omega\cdot m

First, let us find the area of the circular rod.

Area is given as:

A=\pi r^2=3.14\times (0.0019)^2=1.13\times 10^{-5}\ m^2

Now, the resistance of the material is given by the formula:

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

Express this in terms of 'L'. This gives,

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

Now, plug in the given values and solve for length 'L'. This gives,

L=\frac{3.7\ \Omega\times 1.13\times 10^{-5}\ m^2}{1.8\times 10^{-5}\ \Omega\cdot m}\\\\L=\frac{4.181}{1.8}=2.32\ m

Therefore, the length of the material required to make a resistor of 3.7 Ω is 2.32 m.

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