Two wires of the same material have lengths $L$ and $2L$ and cross-sectional areas $4A$ and $A$ respectively. The ratio of their specific resistance would be

$A$ heating element has a resistance of $100\,\Omega$ at room temperature. When it is connected to a supply of $220\,V$,a steady current of $2\,A$ passes through it and the temperature is $500\,^{\circ}C$ higher than room temperature. What is the temperature coefficient of resistance of the heating element?

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

Two wires of equal diameters,of resistivities $\rho_1$ and $\rho_2$ and lengths $l_1$ and $l_2$,respectively,are joined in series. The equivalent resistivity of the combination is

The resistance of the bulb filament is $100 \ \Omega$ at a temperature of $100^{\circ} C$. If its temperature coefficient of resistance is $0.005 \ ^{\circ} C^{-1}$,at what temperature will its resistance become $200 \ \Omega$ (in $^{\circ} C$)?

Consider a block of conducting material of resistivity $\rho$ shown in the figure. Current $I$ enters at $A$ and leaves from $D$. We apply the superposition principle to find the voltage $\Delta V$ developed between $B$ and $C$. The calculation is done in the following steps:
$(i)$ Take current $I$ entering from $A$ and assume it to spread over a hemispherical surface in the block.
$(ii)$ Calculate field $E(r)$ at distance $r$ from $A$ by using Ohm's law $E = \rho j$,where $j$ is the current per unit area at $r$.
$(iii)$ From the $r$ dependence of $E(r)$,obtain the potential $V(r)$ at $r$.
$(iv)$ Repeat $(i)$,$(ii)$ and $(iii)$ for current $I$ leaving $D$ and superpose results for $A$ and $D$.
For current entering at $A$,the electric field at a distance $r$ from $A$ is