# Suppose The Resistance Of A Wire Varies Inversely As The Area Of Its Crosssection. Write A Relation Between Resistance And Area Of Cross-section.

Suppose the radius of the wire is r. Then the area of its cross-section is πr2. If R is the resistance, we are given.

$$R\propto \frac{1}{\Pi r^{2}}\\\Rightarrow R = \frac{k}{\Pi r^{2}} \;or\; k \;= R\Pi r^{2}$$

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