Numerical problems on Resistivity with solution

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

Resistivity - Numerical problems with solution
figure 1

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

Numerical problems on Resistivity - with solution
figure 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

Numerical problems on Resistivity with solution
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