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 m^{2}.

## 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 *= ρ*l/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 *= ρ*l/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} m^{2}

Resistance of the chip = R = ρ*l/A= ( 3.0x 10*^{–5}*Ωm)(10 × 10*^{–3 }*m) /5 × 10*^{–6}*m*^{2}

*=*0.060 Ω