$A$ cylindrical conductor has a uniform cross-section. The resistivity of its material increases linearly from the left end to the right end. If a constant current is flowing through it and at a section at distance $x$ from the left end,the magnitude of the electric field intensity is $E$,which of the following graphs is correct?

The length of a given cylindrical wire is increased by $100\,\%$. Due to the consequent decrease in diameter,the percentage change in the resistance of the wire will be ................ $\%$.

Two wires of equal diameters,of resistivities $\rho_1$ and $\rho_2$ and lengths $l_1$ and $l_2$,respectively,are joined in series. The equivalent resistivity of the combination is

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 $(10^{22}/10^{23}).$

The resistance of the filament of an 'incandescent' bulb increases with an increase in temperature. If $R_{100}$,$R_{60}$,and $R_{40}$ are the resistances of $100 \ W$,$60 \ W$,and $40 \ W$ bulbs at room temperature,respectively,then:

The graph showing the variation of resistance $(R)$ of a metal wire as a function of its diameter $(D)$,while keeping other parameters like length and temperature constant,is: