$A$ metal wire of length $L$ and radius $r$ has a resistance $R$. If a wire of the same metal of length $2L$ and radius $3r$ is taken,then what will be its resistance?

$n$ conducting wires of same dimensions but having resistivities $1, 2, 3, . . . , n$ are connected in series. The equivalent resistivity of the combination is

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.

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

$A$ 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 $1.70 \times 10^{-4} \;^{\circ} C^{-1}$.

$A$ wire of resistance $R$ and radius $r$ is stretched until its radius becomes $r / 2$. If the new resistance of the stretched wire is $x R$,then the value of $x$ is $\qquad$