$A$ 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:

The positive temperature coefficient of resistance is for

$A$ $100 \ W$ tungsten light bulb has a resistance of $250 \ \Omega$ when it is turned $ON$ and $25 \ \Omega$ when turned $OFF$. The ambient room temperature is $25^{\circ} C$. Find the temperature of the filament when the bulb is turned $ON$. (Let $\alpha_{\text{tungsten}} = 4.5 \times 10^{-3} /^{\circ} C$) (in $^{\circ} C$)

$A$ 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?

Two conductors are made of the same material and have the same length. Conductor $A$ is a solid wire of diameter $1 \ mm$. Conductor $B$ is a hollow tube of outer diameter $2 \ mm$ and inner diameter $1 \ mm$. Find the ratio of resistance $R_A$ to $R_B$.

Masses of $3$ wires of same metal are in the ratio $1 : 2 : 3$ and their lengths are in the ratio $3 : 2 : 1$. The electrical resistances are in ratio