Two wires of equal length and equal diameter and having resistivities $\rho_1$ and $\rho_2$ are connected in series. The equivalent resistivity of the combination is . . . . . . .

The variations of resistivity $\rho$ with absolute temperature $T$ for three different materials $X, Y$ and $Z$ are shown in the graph below. Identify the materials $X, Y$ and $Z$.

What is the resistance of a wire of length $5 \, m$ and resistivity $1.7 \times 10^{-8} \, \Omega \cdot m$,given the cross-sectional area is a hollow cylinder with outer radius $r_2 = 10 \, cm$ and thickness $5 \, mm$?

$A$ negligibly small current is passed through a wire of length $15 \ m$ and uniform cross-section $6 \times 10^{-7} \ m^2$,and its resistance is measured to be $5 \ \Omega$. The resistivity of the material at the temperature of the experiment is . . . . . . $\Omega \ m$.

$A$ conducting wire of length $l$,area of cross-section $A$,and electric resistivity $\rho$ is connected between the terminals of a battery. $A$ potential difference $V$ is developed between its ends,causing an electric current. If the length of the wire of the same material is doubled and the area of cross-section is halved,the resultant current would be:

An aluminium (resistivity $\rho = 2.2 \times 10^{-8} \Omega \cdot m$) wire of diameter $1.4 \text{ mm}$ is used to make a $4 \Omega$ resistor. The length of the wire is: (in $\text{ m}$)