Question

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?

Answer 1

5.93 m

Step-by-step 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