The resistance of a wire of uniform diameter $d$ and length $L$ is $R$. The resistance of another wire of the same material but diameter $2d$ and length $4L$ will be

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A:$ Alloys such as constantan and manganin are used in making standard resistance coils.
Reason $R:$ Constantan and manganin have a very small value of temperature coefficient of resistance.
In the light of the above statements, choose the correct answer from the options given below.

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

$A$ heating element using nichrome connected to a $230 \;V$ supply draws an initial current of $3.2 \;A$ which settles after a few seconds to a steady value of $2.8 \;A$. What is the steady temperature of the heating element if the room temperature is $27.0^{\circ} C$ (in $^{\circ} C$)? The temperature coefficient of resistance of nichrome averaged over the temperature range involved is $1.70 \times 10^{-4} \;^{\circ} C^{-1}$.

If $n, e, \tau$ and $m$ represent electron density,charge,relaxation time,and mass of an electron respectively,then the resistance of a wire of length $l$ and cross-sectional area $A$ is given by:

Two conductors are made of the same material and have the same length. Conductor $A$ is a solid wire of diameter $1.0 \, mm$. Conductor $B$ is a hollow tube of outside diameter $2.0 \, mm$ and inside diameter $1.0 \, mm$. The resistance ratio $R_A/R_B$ will be