At room temperature $(27.0^{\circ} C)$,the resistance of a heating element is $100\; \Omega$. What is the temperature (in $^{\circ} C$) of the element if the resistance is found to be $117\; \Omega$,given that the temperature coefficient of the material of the resistor is $1.70 \times 10^{-4}\; ^{\circ} C^{-1}$?

$A$ conducting wire has length $L_1$ and diameter $d_1$. After stretching,the same wire's length becomes $L_2$ and diameter $d_2$. The ratio of resistance before and after stretching is:

Two wires of equal diameters,lengths $l_1, l_2$ and having resistivities $S_1, S_2$ respectively are joined in series. The equivalent resistivity of the combination is

$A$ cylindrical resistor is connected to a battery with emf $5 \ V$. The resistance per unit length varies as $\rho(x) = \rho_0 \left(\frac{x}{L}\right)^\alpha$,where $\rho_0$ and $\alpha$ are constants and $x$ is the distance from one end of the resistor. The product $\rho_0 L$ is $10 \ \Omega$,where $L$ is the length of the resistor. If the thermal power generated by the resistor is $20 \ W$,then the value of $\alpha$ is:

The dimensions of resistivity in terms of $M, L, T$ and $Q$,where $Q$ stands for the dimensions of charge,is:

Assertion: Bending a wire does not affect electrical resistance.
Reason: Resistance of a wire is proportional to the resistivity of the material.