The resistance of a bulb filament is $100\,\Omega$ at a temperature of $100\,^{\circ}C$. If its temperature coefficient of resistance is $0.005\,^{\circ}C^{-1}$,at what temperature will its resistance become $200\,\Omega$?

At what temperature $(^{\circ} C)$ will the resistance of a copper wire become $3$ times its resistance at $0^{\circ} C$? (Given: Temperature coefficient of resistance $\alpha = 4 \times 10^{-3} {}^{\circ} C^{-1}$)

$A$ copper wire is stretched to make it $0.5\%$ longer. The percentage change in its electric resistance if its volume remains unchanged is ................ $\%$

In order to quadruple the resistance of a uniform wire,a part of it is uniformly stretched so that the final length of the wire becomes $1.5$ times the original length. The fractional length of the stretched part is

When a piece of aluminium wire of finite length is drawn through a series of dies to reduce its diameter to half its original value,its resistance will become ........ times.

$A$ 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: