$A$ uniform metal wire carries a current of $2 \, A$ when an ideal cell of $3.4 \, V$ is connected across it. The wire has mass $8.92 \times 10^{-3} \, kg$, density $8.92 \times 10^3 \, kg/m^3$ and resistivity $1.7 \times 10^{-8} \, \Omega m$. Then the length of the wire is (in $m$)

At what temperature will the resistance of a copper wire become three times its value at $0^{\circ}C$? (Temperature coefficient of resistance for copper = $4 \times 10^{-3} \,^{\circ}C^{-1}$)

Resistance of a wire is $8 \Omega$. It is drawn in such a way that it experiences a longitudinal strain of $400 \%$. The final resistance of the wire is (in $\Omega$)

The resistance of a wire is $10\,\Omega$. Its length is increased by $10\%$ by stretching. The new resistance will now be .......... $\Omega$.

$A$ uniform wire of length $l$ and radius $r$ has a resistance of $100\, \Omega$. It is recast into a wire of radius $\frac{r}{2}$. The resistance of the new wire will be ............... $\Omega$.

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