This post presents a few important numerical problems in physics that you can solve using the concepts of resistivity. If you want a quick revision to memorize the resistivity formula then you can check this post on resistivity formula derivation.
Note: Remember that: (1) resistivity is a property of the material (2) the unit of resistivity is ohms times metres and not ohms per metre. (3) In calculations, l must be in metres and A must be in m2.
Resistivity – Numerical problems with solution
1 ] Question1
Use the data for the 32 swg wire given in Figure 1 to calculate a value for the resistivity of nichrome.
Solution: Answer
R = ρl/A
where A = π (d/2)2
Rearranging:
ρ = RA/l
Fetched data from figure 1 for the 32 swg wire.
Substituting R = 18.3 Ω when l = 1.000 m and d = 0.2743 mm:
ρ = (18.3 Ω) π(0.5 × 0.2743 × 10–3 m)2 / 1 m = 1.08 × 10–6 Ω m
2 ] Question 2
A carbon chip of resistivity 3.0x 10–5 Ω m has the dimensions shown in Figure 2.
What resistance does the chip have for a current in the direction shown?
Solution: Answer
Using the formula:
R = ρl/A
Referring figure 2 we get, l = 10 mm = 10 × 10–3 m
and A = 5 mm × 1 mm = 5 × 10–3 m × 1 × 10–3 m
= 5 × 10–6 m2
Resistance of the chip = R = ρl/A= ( 3.0x 10–5Ωm)(10 × 10–3 m) /5 × 10–6m2
=0.060 Ω
