$A$ cylindrical metallic wire is stretched to increase its length. If the resistance of the wire is increased by $4 \%$,then the percentage increase in its length is (in $\%$)

$A$ wire of length $1.0\, m$ and diameter $0.6\, cm$ has a resistance of $3.0 \times 10^{-3}\, \Omega$. What will be the resistance between the faces of a disc made of the same material with diameter $2.0\, cm$ and thickness $1.0\, mm$?

At room temperature $(27^\circ \text{C})$ the resistance of a heating element is $100 \ \Omega$. What is the temperature of the element if the resistance is found to be $137 \ \Omega$,given that the temperature coefficient of the material of the resistor is $1.35 \times 10^{-4} \ ^\circ \text{C}^{-1}$ (in $^\circ \text{C}$)?

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

At room temperature $(27.0^{\circ} C)$,the resistance of a heating element is $100\; \Omega$. What is the temperature (in $^{\circ} C$) of the element if the resistance is found to be $117\; \Omega$,given that the temperature coefficient of the material of the resistor is $1.70 \times 10^{-4}\; ^{\circ} C^{-1}$?