Two wires of same length and thickness having specific resistances $6 \, \Omega \, cm$ and $3 \, \Omega \, cm$ respectively are connected in parallel. The effective resistivity is $\rho \, \Omega \, cm$. The value of $\rho$ to the nearest integer is ..... .

As shown in the schematic below,a rod of uniform cross-sectional area $A$ and length $l$ is carrying a constant current $i$ through it and the voltage across the rod is measured using an ideal voltmeter. The rod is stretched by the application of a force $F$. Which of the following graphs would show the variation in the voltage across the rod as a function of the strain $\varepsilon$ when the strain is small? Neglect Joule heating.

Find the resistance of a cube of edge $60 \text{ cm}$,made of a material of specific resistance $60 \times 10^{-8} \Omega \text{ m}$.

$A$ certain wire has a resistance $R$. The resistance of another wire identical with the first except having twice its diameter is (in $,R$)

$A$ nichrome wire $50 \text{ cm}$ long and $1 \text{ mm}^2$ cross-section carries a current of $4 \text{ A}$ when connected to a $2 \text{ V}$ battery. The resistivity of the nichrome wire in $\Omega \cdot \text{m}$ is:

Two wires are made of two different materials whose specific resistances are in the ratio $2:3$,lengths are in the ratio $3:4$,and cross-sectional areas are in the ratio $4:5$. The ratio of their resistances is: