Question

Suppose the resistance of a wire varies inversely as the area of its cross-section. Write a relation between resistance and area of cross-section.

Answer 1

Hint: Resistance: Resistance is a measure of the opposition to flow of current in any electrical circuit. Resistance is measured by Omega ($\Omega $). Ohms are named after the German physicist George Simon Ohm who studied the relation between the voltage, current and resistance. Formula given by Ohm is:
$V = IR$

Complete step by step answer:
Here we have to calculate the resistance offered by a wire which has length ‘l’ and cross-section of wire ‘A’.
First of all we know that resistance is directly proportional to ‘l’.
$R \propto l$ …(1)
And then resistance is inversely proportional to ‘A’
 $R \propto \dfrac{1}{A}$ …(2)
After combining the equation (1) and (2) then
$R = \rho \dfrac{l}{A}$
Here $\rho $is the resistivity. And the SI unit of $\rho $ is $\Omega - m$.

Note: To increase the resistance of any circuit we use resistors. Resistors may be joined in the series of the circuits or parallel to the circuits.