The temperature coefficient of resistance of a resistor wire is $0.00125\,^{\circ}C^{-1}$. At $300\,K$,its resistance is $1\,\Omega$. At what temperature in $K$ will its resistance be $2\,\Omega$?

$A$ silver wire has a resistance of $2.1 \Omega$ at $27.5^{\circ} C$ and a resistance of $2.7 \Omega$ at $100^{\circ} C$. Then the temperature coefficient of the resistivity of silver will be . . . . . . .

The conductivity of a conductor decreases with temperature because,on heating:

$A$ 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:

$A$ given piece of wire of length $l$ and radius $r$ and resistance $R$ is stretched uniformly to a wire of radius $\frac{r}{2}$. Its new resistance is .................. $R$.

Masses of three wires of copper are in the ratio of $1 : 3 : 5$ and their lengths are in the ratio of $5 : 3 : 1$. The ratio of their electrical resistance is . . . . . . .