In order to quadruple the resistance of a uniform wire,a part of its length $x$ was uniformly stretched till the final length of the entire wire was $1.5$ times the original length $l$. The fraction of the wire that was stretched,$x/l$,is equal to:

$A$ conducting wire of length $l$,area of cross-section $A$,and electric resistivity $\rho$ is connected between the terminals of a battery. $A$ potential difference $V$ is developed between its ends,causing an electric current. If the length of the wire of the same material is doubled and the area of cross-section is halved,the resultant current would be:

The resistance of a wire at $30^{\circ}C$ is $10\, \Omega$. To increase the resistance of the wire by $10\%$,the temperature should be .......... $^{\circ}C$. The temperature coefficient of resistance of the material of the wire is $0.002\, ^{\circ}C^{-1}$.

$A$ 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 increases with:

The alloys constantan and manganin are used to make standard resistance due to they have