The resistance of the bulb filament is $100 \ \Omega$ at a temperature of $100^{\circ} C$. If its temperature coefficient of resistance is $0.005 \ ^{\circ} C^{-1}$,at what temperature will its resistance become $200 \ \Omega$ (in $^{\circ} C$)?

Consider a thin square sheet of side $L$ and thickness $t$,made of a material of resistivity $\rho$. The resistance between two opposite faces,shown by the shaded areas in the figure is

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

The coefficient of linear expansion of the material of a resistor is $\alpha$. Its temperature coefficient of resistivity and resistance are $\alpha_\rho$ and $\alpha_R$ respectively. Then the correct relation is:

Two metal wires of identical dimensions are connected in series. If $\sigma_1$ and $\sigma_2$ are the conductivities of the metal wires respectively,the effective conductivity of the combination is

$A$ $1\,m$ long wire is broken into two unequal parts $X$ and $Y$. The $X$ part of the wire is stretched into another wire $W$. The length of $W$ is twice the length of $X$ and the resistance of $W$ is twice that of $Y$. Find the ratio of the length of $X$ to the length of $Y$.