We have two wires $A$ and $B$ of the same mass and same material. The diameter of wire $A$ is half that of wire $B$. If the resistance of wire $A$ is $24 \, \Omega$,then the resistance of wire $B$ will be ................ $\Omega$.

Which of the following graphs represents the variation of resistivity ( $\rho$ ) with temperature $(T)$ for copper?

The resistance of a tungsten wire at $150^{\circ} C$ is $133 \Omega$. The temperature coefficient of resistance is $0.0045^{\circ} C^{-1}$. The resistance of this wire at $500^{\circ} C$ is: (in $\Omega$)

$A$ cylindrical resistor is connected to a battery with emf $5 \ V$. The resistance per unit length varies as $\rho(x) = \rho_0 \left(\frac{x}{L}\right)^\alpha$,where $\rho_0$ and $\alpha$ are constants and $x$ is the distance from one end of the resistor. The product $\rho_0 L$ is $10 \ \Omega$,where $L$ is the length of the resistor. If the thermal power generated by the resistor is $20 \ W$,then the value of $\alpha$ 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 ............... $\Omega$.

What is the resistivity of a perfect conductor?