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:

Resistance of a tungsten wire at $150\,^{\circ}C$ is $133\,\Omega$. Its resistance temperature coefficient is $0.0045\,^{\circ}C^{-1}$. The resistance of this wire at $500\,^{\circ}C$ will be .............. $\Omega$.

The electrical resistance of an iron wire is $R$. If both its length and radius are doubled,then:

This question contains statement-$1$ and statement-$2$. Of the four choices given after the statements,choose the one that best describes the two statements.
statement-$1$: The temperature dependence of resistance is usually given as $R=R_{0}(1+\alpha \Delta t)$. The resistance of a wire changes from $100 \; \Omega$ to $150 \; \Omega$ when its temperature is increased from $27^{\circ} C$ to $227^{\circ} C$. This implies that $\alpha=2.5 \times 10^{-3} /^{\circ} C$.
statement-$2$: $R=R_{0}(1+\alpha \Delta t)$ is valid only when the change in the temperature $\Delta t$ is small and $\Delta R=(R-R_{0}) << R_{0}$.

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

$A$ nichrome wire $50 \text{ cm}$ long and $1 \text{ mm}^2$ cross-section carries a current of $4 \text{ A}$ when connected to a $2 \text{ V}$ battery. The resistivity of the nichrome wire in $\Omega \cdot \text{m}$ is: