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 resistor? The resistivity of this material is 1.8 × 10−5 Ω · m .

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) =

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

Area is given as:

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

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

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

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