There are three copper wires of length and cross-sectional area $$\left( {L,A} \right),\left( {2L,\frac{A}{2}} \right)\left( {\frac{L}{2},2A} \right).$$      In which case is the resistance minimum ?

Solution :
The relation between length and area is
$$R = \frac{{\rho l}}{A}\,......\left( {\text{i}} \right)$$
where, $$\rho $$ being specific resistance is the proportionality constant and depends on nature of material.
(i) Length $$ = \frac{L}{2},$$   area $$ = 2\,A$$
Putting in Eq. (i), we have
$$R = \frac{{\rho \left( {\frac{L}{2}} \right)}}{{2A}} = \frac{{\rho L}}{{4A}}$$
(ii) Length $$= L,$$  area $$ = A$$
Putting in Eq. (i), we have
$$R = \frac{{\rho l}}{A}$$
(iii) Length $$ = 2L,$$  area $$ = \frac{A}{2}$$
Putting in Eq. (i), we have
$$R = \rho \frac{{2L}}{{\frac{A}{2}}} = \frac{{4\rho L}}{A}$$
As it is understood from above, resistance is minimum only in option (B).