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

Two conductors have the same resistances at $0^{\circ} C$ but their temperature coefficients of resistance are $\alpha_1$ and $\alpha_2$. The respective temperature coefficients for their series and parallel combinations are :

Choose the correct alternative:
$(a)$ Alloys of metals usually have (greater/less) resistivity than that of their constituent metals.
$(b)$ Alloys usually have much (lower/higher) temperature coefficients of resistance than pure metals.
$(c)$ The resistivity of the alloy manganin is nearly independent of/ increases rapidly with increase of temperature.
$(d)$ The resistivity of a typical insulator (e.g.,amber) is greater than that of a metal by a factor of the order of $(10^{22}/10^{23}).$

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:

In the following diagram,the lengths of wires $AB$ and $BC$ are equal,but the radius of wire $AB$ is double that of $BC$. The ratio of the potential gradient on wires $AB$ and $BC$ will be (wires are made of the same material):

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$.