(a) Write the relationship between resistivity and resistance of a cylindrical conductor of length l and area of cross-section A. Hence derive the SI unit of resistivity.

(b) Why are alloys used in electrical heating devices?

(a) Resistance of a cylindrical conductor is given by,

$\text R = \text ρ \dfrac{\text l}{\text A}$

Then,

$\text {SI unit of R} = \text {SI unit of ρ} \times \dfrac{\text {SI unit of l}}{\text {SI unit of A}} \\[1em] \Rightarrow \text {SI unit of ρ} = \dfrac {\text {SI unit of R}\times \text {SI unit of A}}{\text {SI unit of l}} \\[1em] = \dfrac{\text Ω \times \text m^2 }{\text m} \\[1em] \Rightarrow \text {SI unit of ρ} = \text {Ω.m}$

Hence, SI unit of ρ is Ω.m.

(b) Alloys are used in electrical heating devices because :

• they have relatively high resistivity, so they produce a large amount of heat for a given current and voltage;
• they have high melting points, so they do not melt at the high temperatures reached during heating;
• they are resistant to oxidation and corrosion at high temperatures, so the heating element lasts longer;
• their mechanical strength and ductility are suitable for making durable coils.

Pure metals (like copper) have low resistivity and oxidise or melt easily, so they are unsuited for heating elements.