The resistance of a conductor at $20\,^{\circ}C$ and $500\,^{\circ}C$ is $20\,\Omega$ and $60\,\Omega$ respectively. At what temperature will the resistance be $25\,\Omega$?

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

Wires $P$ and $Q$ have the same resistance at room temperature. When heated,the resistance of $P$ increases and that of $Q$ decreases. We conclude that:

Two solid conductors are made of the same material,have the same length,and have the same resistance. One of them has a circular cross-section of area $A_{1}$ and the other has a square cross-section of area $A_{2}$. The ratio $\frac{A_{1}}{A_{2}}$ is

The resistance of a wire is $20 \, \Omega$. It is stretched such that its length becomes three times its original length. The new resistance of the wire will be ............. $ \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: