A carbon rod with a radius of 2.1 mm is used to make a resistor. The resistivity of this material is 3.2 * 10-5 Ω · m. What length of the carbon rod should be used to make a 13.7 Ω resistor?

5.93 m

Explanation:

The carbon rod has a radius of 2.1 mm; it can be converted to meter by

1 m = 1000 mm

1 m : 1000 = 1 mm

2.1 mm = 2.1 * 1 mm = 2.1 * 1:1000 m = 0.0021 m

using the formula for resistance of a wire

R = ρl:A, where R is the resistance of the carbon rod in ohms, ρ is resistivity in ohms. m, l is the length of the rod and A is the cross sectional area in m².

A = π r²

Make l the subject of the formula by cross multiplying

RA = ρl

divide both side by ρ

RA:ρ = ρl:ρ

RA:ρ = l

substitute the values in

13.7 * 0.0021 * 0.0021 * 3.142 : 3.2 * 10^-5 = 5.93 m