An aluminium wire is stretched to make its length $0.4 \%$ larger. Then the percentage change in resistance is $.....\,\%$.

The resistance of a wire at $300 \, K$ is found to be $0.3 \, \Omega$. If the temperature coefficient of resistance of the wire is $1.5 \times 10^{-3} \, K^{-1}$, the temperature at which the resistance becomes $0.6 \, \Omega$ is: (in $K$)

What is the resistance of a cubic block of length $50 \, cm$ having a resistivity of $50 \times 10^{-8} \, \Omega m$?

$A$ 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:

Consider a thin square sheet of side $L$ and thickness $t$,made of a material of resistivity $\rho$. The resistance between two opposite faces,shown by the shaded areas in the figure is

$A$ 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 . . . . . . $\Omega \ m$.