$A$ cylinder of a material is $10\, cm$ long and has a cross-section of $2\, cm^{2}$. If its resistance along the length is $20\, \Omega$,what will be its resistivity in number and units?

$(a)$ Why are copper or aluminium wires generally used for electrical transmission and distribution purposes?
$(b)$ Two wires,one of copper and the other of manganin,have equal lengths and equal resistances. Which wire is thicker? Given that the resistivity of copper is lower than that of manganin.

Which one of the following is true according to Ohm's law?

$(a)$ $A$ Nichrome wire of length $L$ and radius $r$ has a resistance of $10 \, \Omega$. How would the resistance of the wire change when:
$(i)$ only the length of the wire is doubled?
$(ii)$ only the diameter of the wire is doubled? Justify your answer.
$(b)$ Why are the elements of electrical heating devices made up of alloys?

The electric current flowing through any conductor is directly proportional to the electric potential difference across the conductor. Which law is this?

Resistivity of two elements $A$ and $B$ are $1.62 \times 10^{-8} \, \Omega m$ and $520 \times 10^{-8} \, \Omega m$ respectively. Out of these two,name the element that can be used to make
$(i)$ filament of electric bulb.
$(ii)$ wires for electrical transmission lines. Justify your answer in each case.