The resistance of a wire is $2.5 \Omega$ at a temperature $373 \ K$. If the temperature coefficient of resistance of the material of the wire is $3.6 \times 10^{-3} \ K^{-1}$,its resistance at a temperature $273 \ K$ is nearly: (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 conductor is $5\,\Omega$ at $50\,^{\circ}C$ and $6\,\Omega$ at $100\,^{\circ}C$. Its resistance at $0\,^{\circ}C$ is ................ $\Omega$.

$A$ wire of radius $r$ has resistance $R$. If it is stretched to a radius of $\frac{3r}{4}$,its resistance becomes

The resistances of a wire at temperatures $t\,^oC$ and $0\,^oC$ are related by:

$A$ cylindrical wire $P$ has resistance $10 \ \Omega$. $A$ second wire $Q$ has length and diameter half that of $P$. If the material of both the wires is same,then the resistance of wire $Q$ is (in $\Omega$)