The length of a metallic wire is increased by $20 \%$ and its area of cross-section is reduced by $4 \%$. The percentage change in resistance of the metallic wire is $.......$ (in $\%$)

Two metal wires of identical dimensions are connected in series. If $\sigma_1$ and $\sigma_2$ are the conductivities of the metal wires respectively,the effective conductivity of the combination is

The length and area of cross-section of a copper wire are respectively $30 \ m$ and $6 \times 10^{-7} \ m^2$. If the resistivity of copper is $1.7 \times 10^{-8} \ \Omega \ m$,then the resistance of the wire is (in $Omega$)

Two different conductors have the same resistance at $0\,^{\circ}C.$ It is found that the resistance of the first conductor at $t_1\,^{\circ}C$ is equal to the resistance of the second conductor at $t_2\,^{\circ}C.$ The ratio of the temperature coefficients of resistance of the conductors,$\frac{\alpha_1}{\alpha_2}$ is

The resistance of a wire is $5\, \Omega$ at $50\, ^\circ C$ and $6\, \Omega$ at $100\, ^\circ C$. The resistance of the wire at $0\, ^\circ C$ will be .............. $\Omega$.

$A$ uniform wire of length $l$ and radius $r$ has a resistance of $100\, \Omega$. It is recast into a wire of radius $\frac{r}{2}$. The resistance of the new wire will be ............... $\Omega$.