What is meant by resistance of a conductor? Name and define its $SI$ unit. List the factors on which the resistance of a conductor depends. How is the resistance of a wire affected if
$(i)$ its length is doubled,
$(ii)$ its radius is doubled?

(N/A) Resistance is the property of a conductor to oppose the flow of electric current through it.
The $SI$ unit of resistance is $Ohm$ ($\Omega$). One $Ohm$ is defined as the resistance of a conductor through which a current of $1$ $Ampere$ flows when a potential difference of $1$ $Volt$ is applied across its ends.
The factors on which the resistance of a conductor depends are:
$1$. Length of the conductor $(l)$
$2$. Area of cross-section $(A)$
$3$. Nature of the material (resistivity, $\rho$)
$4$. Temperature of the conductor
$(i)$ Since resistance $R \propto l$, if the length is doubled, the resistance becomes $2$ times the original value.
$(ii)$ Since resistance $R \propto \frac{1}{A}$ and $A = \pi r^2$, if the radius $r$ is doubled, the area $A$ becomes $4$ times $(A' = \pi(2r)^2 = 4\pi r^2)$. Consequently, the resistance becomes $\frac{1}{4}$th of its original value.