Pencil “lead” is actually carbon. What is the resistance of the 0.680 mmdiameter, 4.40 cmlong lead from a mechanical pencil?
3 Answers

RickB was almost correct. You multiply the resistivity by the length and divide by the crosssectional area. A long, thin resistor will have a greater resistance than a short, wide resistor made of the same material.
Also, different forms of carbon have different resistivity. You’ll want to look up the resistivity of graphite.

Look up the resistivity of carbon in a table.
Multiply by the pencil lead’s crosssectional area (remember A=πr²).
Divide by the pencil lead’s length.

Resistivity of Carbon (graphite) constant at RT = 3.5e 5
Formulas:
Area = (pi(r^2))
r = (0.680/2/(1000))
pi = 3.14
Resistivity = Res. Constant (σ) * Length (L) / Area (A)
Resistivity = 3.5e 5 * .0440 m / 3.62984e 7 = 4.2426 Ω