Question

The resistance of a conductor is:
A. Inversely proportional to the length
B. Directly proportional to the square of the radius
C. Inversely proportional to the square of the radius
D. Directly proportional to the square root of the length

Answer 1

Resistance is the opposition to the flow of charges in a circuit. It depends on the length, area of cross section, resistivity and the temperature of the conductor. i.e. the relationship of various components of resistance can be given as $R=\rho\dfrac{L}{A}$ .

Formula used : $R=\rho\dfrac{L}{A}$

Complete step-by-step answer :
Electrical resistance is the opposition to the flow of current in the conductor. It is the reciprocal of electrical conductance.
We know that the resistance of the conductor depends on the material used, size and shape of the material, temperature of the material.
Thus that the resistance of the conductor depends on the material used, length of the material and area of material used .i.e.$R=\rho\dfrac{L}{A}$ where $\rho$ is the specific resistance or the resistivity, $L$ is the length of the resistance in meters and $A$ is the area of the resistance in square meter. The resistance also depends on the temperature of the conductor, when the temperature rises the number of photons in the conductor increases, and hence the collision between electrons and photons. Thus, increases in the temperature, increases the resistance of the conductor.
Clearly,
$Resistance \propto \dfrac{1}{area\;of\;cross\;section}$
Since resistors are cylindrical, $area\;of\;cross\;section=r^{2}$
$R\propto\dfrac{1}{r^{2}}$
Hence the answer is C. Inversely proportional to the square of the radius.

Note :The resistance of the conductor depends on the following: the material used, size and shape of the material. Also, we can write mathematically,$R\propto L$,$R\propto \dfrac{1}{r^{2}}$, $R\propto T$ and $R\propto \rho$. Also resistance are usually colour coded. They can be measured using a digital or analog multimeter or using ohmmeter.